1.
5, 11, 24, 51, 106, ___
Correct Answer
A. 217
Explanation
The next number in the sequence is 217.
This sequence follows a pattern where each number is the sum of the previous number and the square of its position in the sequence.
Here's the breakdown:
Position 1: 5 (1^2 + previous number = 0 + 5)
Position 2: 11 (2^2 + previous number = 4 + 5)
Position 3: 24 (3^2 + previous number = 9 + 11)
Position 4: 51 (4^2 + previous number = 16 + 24)
Position 5: 106 (5^2 + previous number = 25 + 51)
Position 6: 217 (6^2 + previous number = 36 + 106)
Following this pattern, the number at position 6 (the next number in the sequence) would be 217 (36 + 106).
2.
3, 10, 31, 80, 171, ___
Correct Answer
A. 318
Explanation
The next number in the sequence is 318.
Here's the logic behind the sequence:
Each term is obtained by taking the previous term and adding the product of its position in the sequence and the previous term itself.
Let's break it down for the first few terms:
Position 1: Starting number, so no addition (3)
Position 2: 3 (previous term) + (1 * 3) = 10 (position 1 * previous term)
Position 3: 10 (previous term) + (2 * 10) = 30 (position 2 * previous term)
Position 4: 31 (previous term) + (3 * 31) = 80 (position 3 * previous term)
Position 5: 80 (previous term) + (4 * 80) = 171 (position 4 * previous term)
Following this pattern:
Position 6: 171 (previous term) + (5 * 171) = 318 (position 5 * previous term)
Therefore, the next number in the sequence is 318.
3.
8, 12, 16, 20, 24, _____
Correct Answer
A. 28
Explanation
The next number in the sequence is 28.
This sequence appears to be increasing by adding 4 consecutively.
Starting number: 8
4: 12
4: 16
4: 20
4: 24
Following the pattern, the next number would be:
4: 24 + 4 = 28
4.
3,9,27,____,243
Correct Answer
D. 81
Explanation
The next number in the sequence is 81.
This sequence follows a simple pattern: each number is the previous number multiplied by 3.
3 (starting number)
3 * 3 = 9
9 * 3 = 27
27 * 3 = 81
81 * 3 = 243
Following this pattern, the next number in the sequence is 81.
5.
2, 3, 5, 7, 9, ___, 13, 15
Correct Answer
B. 11
Explanation
This sequence consists of prime numbers. The sequence starts with the prime numbers in ascending order, skipping 2, then 3, then 5, then 7, and then 11. Following this pattern, the next prime number after 11 is 13.
So, the missing number in the sequence is 11.
Therefore, the complete sequence is:
2, 3, 5, 7, 9, 11, 13, 15
6.
5, 10, 20, _______, 80
Correct Answer
A. 40
Explanation
To identify the pattern in the sequence, let's examine the relationship between consecutive terms:
- 10 is double 5.
- 20 is double 10.
- The next term is not immediately obvious based on a simple doubling pattern.
However, if we consider each term as the previous term multiplied by an increasing power of 2, we can derive the sequence:
- 5 Ã— 2 = 10
- 10 Ã— 2 = 20
- 20 Ã— 2 = 40
So, the missing term in the sequence is 40.
Therefore, the complete sequence is:
5, 10, 20, 40, 80
7.
240, 120, 60, 30, ______
Correct Answer
A. 15
Explanation
To identify the pattern in the sequence, let's examine the relationships between consecutive terms:
- 240 ÷ 2 = 120
- 120 ÷ 2 = 60
- 60 ÷ 2 = 30
It seems each term is obtained by dividing the previous term by 2.
Following this pattern, the next term would be:
- 30 ÷ 2 = 15
So, the missing term in the sequence is 15.
Hence, the complete sequence is:
240, 120, 60, 30, 15
8.
Identify the inappropriate term in the following number category:
2, 5, 8, 11, 14, 17, 23
Correct Answer
D. 23
Explanation
In the sequence provided:
2, 5, 8, 11, 14, 17, 23
The sequence appears to be increasing by 3 for the first six terms, but then there's an abrupt change from 17 to 23, which increases by 6 instead of 3.
Therefore, the inappropriate term in the sequence is 23.
9.
3, 4, 9, 16, 81, 256, _______
Correct Answer
B. 6561
Explanation
In the sequence:
3, 4, 9, 16, 81, 256, _____
We can see that the pattern alternates between squares of 3 and 4:
32=9
42=16
92=81
162=256
Following this pattern, the next term should indeed be the square of 81:
812=6561.
Therefore, the missing term in the sequence is 6561.
Hence, the complete sequence is:
3, 4, 9, 16, 81, 256, 6561.
10.
Identify the inappropriate term in the following number category.
905, 180, 175, 35, 30, 6
Correct Answer
A. 6
Explanation
In the sequence:
905, 180, 175, 35, 30, 6
We observe the following pattern:
From 905 to 180, there's a division by 5.
From 180 to 175, there's a subtraction of 5.
From 175 to 35, there's a division by 5.
From 35 to 30, there's a subtraction of 5.
From 30 to 6, there's a division by 5.
All terms in the sequence except for 6 are divisible by 5. However, 6 breaks this pattern, as it is not divisible by 5.
Therefore, the inappropriate term in the sequence is 6.
11.
Identify the inappropriate term in the following alternating number category.
3, 2, 8, 9, 13, 22, 18, 32, 23, 42
Correct Answer
B. 9
Explanation
There are 2 series : 3, 8, 13, 18, 23 and 2, 9, 22, 32, 42. In the first series, the difference between the numbers is 5. In the second series, 9 is inconsistent with the numbers as the difference 9 and 2 is 7, but the rest of the numbers have a difference of 10. So, the number 9 should be replaced by 12 to have a proper series.
12.
Identify the inappropriate term in the following number category.
12,16,20,24,32,36,40
Correct Answer
D. 32
Explanation
The inappropriate term in the number category is 32.
Here's why:
The sequence follows a pattern of adding 4 to the previous number.
Starting with 12:
12 + 4 = 16
16 + 4 = 20
20 + 4 = 24
24 + 4 = 28 (expected number)
However, the sequence has 32 instead of 28.
Then it continues the pattern:
32 + 4 = 36
36 + 4 = 40
Therefore, 32 disrupts the pattern of adding 4 and should be replaced with 28 to maintain consistency.
13.
2, 3, 5, 5, 11, 9, 23, ____
Correct Answer
C. 17
Explanation
There are two sequences in this series.
2,5,11,23.....
3,5,9.......
The first series follows a specific sequence:
5-2=3
3*2=6
6+5=11
11-5=6
6*2=12
11+12=23
The second series follows a specific sequence:
5-3=2
9-5=4
The difference increases by a factor of 22
Thus, the next difference would be 8
So, the number in that sequence should be 17 for it to have a difference of 8 since 17-9=8.
14.
Identify the inappropriate term in the following number category.
89, 78, 86, 80, 85, 82, 83
Correct Answer
A. 83
Explanation
The sequence is –11, +9, –7, +5, –3, +1 So, 86 is wrong and should be replaced by 87.
89 - 11 = 78
78 + 9 = 87
87 - 7 = 80
80 + 5 = 85
85 - 3 = 82
82 + 1 = 83
So, based on the given sequence of operations, the corrected sequence would be:
89, 78, 87, 80, 85, 82, 83
15.
In an AP, if the first term is 5 and the common difference is 3, what is the seventh term?
Correct Answer
D. 23
Explanation
Let's find the seventh term of the arithmetic progression (AP).
Formula for nth term in AP:
The nth term (Tn) in an AP can be found using the formula:
Tn = a + (n - 1) * d
where:
Tn is the nth term
a is the first term
n is the term number (in this case, 7)
d is the common difference
Given values:
a (first term) = 5
d (common difference) = 3
n (term number) = 7 (we need to find the seventh term)
Finding the seventh term:
Plug the values into the formula:
T7 = 5 + (7 - 1) * 3
T7 = 5 + (6) * 3
T7 = 5 + 18
T7 = 23
Therefore, the seventh term in the AP is 23.
Answer: d) 23
16.
What is the nth term of the arithmetic progression 2,5,8,11,…2,5,8,11,…?
Correct Answer
A. 3n−1
Explanation
The nth term of the arithmetic progression 2, 5, 8, 11, ... is A) 3n - 1.
Here's why:
Identifying the pattern: We can see that the sequence increases by 3 each time (5 - 2 = 8 - 5 = 11 - 8 = 3). This constant value of 3 is the common difference (d) of the arithmetic progression.
Formula for nth term: The general formula for the nth term (Tâ‚™) in an arithmetic progression is:
Tâ‚™ = a + (n - 1) * d
where:
a is the first term of the sequence (in this case, a = 2).
n is the term number you're interested in (nth term).
d is the common difference (in this case, d = 3).
Finding the nth term: We can plug the known values into the formula to find the expression for the nth term.
Tâ‚™ = 2 + (n - 1) * 3
Expanding the bracket:
Tâ‚™ = 2 + 3n - 3
Combining like terms:
Tâ‚™ = 3n - 1
Therefore, the nth term of the arithmetic progression is 3n - 1. This matches option A.
17.
7, 12, 19, 28, 39, ? ,
Correct Answer
D. 52
Explanation
To find the missing term in the sequence, let's analyze the pattern:
Starting with 7:
- Adding 5 to 7 gives 12.
- Adding 7 to 12 gives 19.
- Adding 9 to 19 gives 28.
- Adding 11 to 28 gives 39.
We can observe that the difference between consecutive terms increases by 2 each time.
So, to find the next term:
- We add 13 to 39.
Thus, the missing term in the sequence is 52.
Therefore, the complete sequence is:
7, 12, 19, 28, 39, 52.
18.
2, 8, 18, 32, 50, ___
Correct Answer
C. 72
Explanation
To find the pattern in the sequence, let's analyze the differences between consecutive terms:
- From 2 to 8, there's an increase of 6.
- From 8 to 18, there's an increase of 10.
- From 18 to 32, there's an increase of 14.
- From 32 to 50, there's an increase of 18.
We can observe that the differences between consecutive terms are increasing by 4 each time. This suggests a quadratic pattern.
To find the next term, we add 4 to the difference between 32 and 50 (which is 18):
50 + 18 + 4 = 72.
So, the missing term in the sequence is 72.
Therefore, the complete sequence is:
2, 8, 18, 32, 50, 72.
19.
4, 16, 36, ? , 100,
Correct Answer
A. 64
Explanation
To find the missing term in the sequence, let's analyze the pattern:
Starting with 4:
- 4 is (2^2).
- 16 is (4^2).
- 36 is (6^2).
- 100 is (10^2).
We can observe that each term is a square of consecutive even numbers: 2, 4, 6, 10.
So, following this pattern, the missing term should be (8^2 = 64).
Therefore, the complete sequence is:
4, 16, 36, 64, 100.
20.
5, 16, 51, 158, ? ,
Correct Answer
B. 481
Explanation
Starting with 5:
- 16 is (5 times 3 + 1).
- 51 is (16 times 3 + 3).
- 158 is (51 times 3 + 5).
Following this pattern, the next term should be:
- (158 times 3 + 7 = 481).
Therefore, the missing term in the sequence is 481.
Hence, the complete sequence is:
5, 16, 51, 158, 481.
21.
255, 367, 479, 591, ____
Correct Answer
D. 703
Explanation
To find the missing term in the sequence, let's analyze the pattern:
Starting with 255:
- The difference between consecutive terms appears to be 112 (367 - 255 = 112, 479 - 367 = 112, and so on).
Following this pattern:
- 591 + 112 = 703.
Therefore, the missing term in the sequence is 703.
Hence, the complete sequence is:
255, 367, 479, 591, 703.
22.
2, 2.4, 2.8, 3.2, 3.6, ____
Correct Answer
B. 4.0
Explanation
To find the next term in the sequence, let's analyze the pattern:
Starting with 2:
- Each subsequent term is obtained by adding 0.4.
Following this pattern:
- (3.6 + 0.4 = 4.0).
Therefore, the next term in the sequence is 4.0.
Hence, the complete sequence is:
2, 2.4, 2.8, 3.2, 3.6, 4.0.
23.
5,15,25,35,_____
Correct Answer
C. 50
Explanation
In this sequence, each term increases by 10.
So, following this pattern:
- 35 + 10 = 45.
Therefore, the next term in the sequence is 45.
Hence, the complete sequence is:
5, 15, 25, 35, 45.
24.
3, 12, 27, 48, 75, 108, ?
Correct Answer
B. 147
Explanation
To find the pattern in the sequence, let's analyze the differences between consecutive terms:
- From 3 to 12, there's an increase of (12 - 3 = 9).
- From 12 to 27, there's an increase of (27 - 12 = 15).
- From 27 to 48, there's an increase of (48 - 27 = 21).
- From 48 to 75, there's an increase of (75 - 48 = 27).
- From 75 to 108, there's an increase of (108 - 75 = 33).
It appears that the differences between consecutive terms are increasing by (6 = 3 times 2).
So, let's find the next difference:
- (33 + 6 = 39).
To find the next term, we add this difference to the last term:
- (108 + 39 = 147).
Therefore, the missing term in the sequence is 147.
Hence, the complete sequence is:
3, 12, 27, 48, 75, 108, 147.
25.
2, 3, 10, 15, 26, ______
Correct Answer
B. 35
Explanation
From the given sequence:
2, 3, 10, 15, 26, ?
The differences between consecutive terms are:
3 - 2 = 1, 10 - 3 = 7, 15 - 10 = 5, 26 - 15 = 11.
The differences between these differences are:
7 - 1 = 6, 5 - 7 = -2, 11 - 5 = 6.
If we follow the pattern where the differences between differences alternate between 6 and -2, and the next difference is -2, then to find the next term, we would need to subtract 2 from 11.
Thus, 26+11−2=35.
Therefore, according to this pattern, the missing term in the sequence is 35.
26.
2, 9, 35, 98, 222, ?
Correct Answer
A. 437
Explanation
Following the provided pattern, each term is obtained by adding the cube of the term number minus 1:
- (2 + (2^3 - 1) = 9)
- (9 + (3^3 - 1) = 35)
- (35 + (4^3 - 1) = 98)
- (98 + (5^3 - 1) = 222)
So, following the pattern:
- (222 + (6^3 - 1) = 222 + (216 - 1) = 437)
Therefore, the missing term in the sequence is 437.
Hence, the complete sequence is:
2, 9, 35, 98, 222, 437.
27.
0, 7, 26, ? , 124, 215
Correct Answer
C. 63
Explanation
Thank you for providing the pattern.
Following the pattern where each term is obtained by subtracting 1 from the cube of the term number:
- (0^3 - 1 = -1)
- (1^3 - 1 = 0)
- (2^3 - 1 = 7)
- (3^3 - 1 = 26)
The next term should be:
- (4^3 - 1 = 64 - 1 = 63)
Therefore, the missing term in the sequence is 63.
Hence, the complete sequence is:
0, 7, 26, 63, 124, 215.
28.
4, 7, 11, 18, 29, 47, ____ , 123, 199
Correct Answer
C. 76
Explanation
From the given sequence:
4, 7, 11, 18, 29, 47, ?, 123, 199
Let's examine the pattern:
- 4 + 3 = 7
- 7 + 4 = 11
- 11 + 7 = 18
- 18 + 11 = 29
- 29 + 18 = 47
Following this pattern, each term is obtained by adding the previous two terms:
- 47 + 29 = 76
So, the next term in the sequence is 76.
Therefore, the missing term in the sequence is 76.
Hence, the complete sequence is:
4, 7, 11, 18, 29, 47, 76, 123, 199.
29.
1, 2, 10, 37, 101, _______
Correct Answer
A. 226
Explanation
To identify the pattern in the sequence, let's analyze the differences between consecutive terms:
- From 1 to 2, there's an increase of (2 - 1 = 1).
- From 2 to 10, there's an increase of (10 - 2 = 8).
- From 10 to 37, there's an increase of (37 - 10 = 27).
- From 37 to 101, there's an increase of (101 - 37 = 64).
It seems that the differences between consecutive terms are not following a straightforward arithmetic progression.
However, let's examine the differences between these differences:
- The difference between 2 and 1 is -1.
- The difference between 10 and 2 is 8.
- The difference between 37 and 10 is 27.
- The difference between 101 and 37 is 64.
The differences between these differences are increasing by 9: -1, 8, 27, 64.
Following this pattern, the next difference would be 125.
Adding 125 to the last term in the sequence, 101, gives us 226.
Therefore, the missing term in the sequence is 226.
Hence, the complete sequence is:
1, 2, 10, 37, 101, 226.
30.
10080, 10080, 5040, 1680, 420, ____
Correct Answer
D. 84
Explanation
To identify the pattern in the sequence, let's examine the differences between consecutive terms:
- From 10080 to 10080, the difference is 0.
- From 10080 to 5040, the difference is 5040.
- From 5040 to 1680, the difference is 3360.
- From 1680 to 420, the difference is 1260.
The pattern doesn't seem consistent in terms of the differences.
Let's explore a different approach:
The numbers in the sequence seem to be decreasing by a factor each time. Let's divide each term by a factor to see if we can find a consistent pattern:
- (10080/ 2 = 5040)
- (5040/ 3 = 1680)
- (1680/ 4 = 420)
So, it appears that each term is being divided by successive integers starting from 2.
Following this pattern:
- (420/ 5 = 84)
Therefore, the next term in the sequence is 84.
Hence, the complete sequence is:
10080, 10080, 5040, 1680, 420, 84.
31.
2, 12, 36, 80, 150, 252, ? ,
Correct Answer
C. 392
Explanation
Thank you for providing the pattern.
Following the pattern (n^3 + n^2) or (n^2 times (n + 1)), where (n) is the term number:
- For (n = 1): (1^3 + 1^2 = 1 + 1 = 2)
- For (n = 2): (2^3 + 2^2 = 8 + 4 = 12)
- For (n = 3): (3^3 + 3^2 = 27 + 9 = 36)
- For (n = 4): (4^3 + 4^2 = 64 + 16 = 80)
- For (n = 5): (5^3 + 5^2 = 125 + 25 = 150)
- For (n = 6): (6^3 + 6^2 = 216 + 36 = 252)
So, following this pattern:
- For (n = 7): (7^3 + 7^2 = 343 + 49 = 392)
Therefore, the next term in the sequence is 392.
Hence, the complete sequence is:
2, 12, 36, 80, 150, 252, 392.