The Arithmetic Progression Test! Math Quiz

2.

The number of terms in the A.P. 2, 5, 8,….., 59 is

20
19
12
25

Correct Answer

A. 20

Explanation

The given arithmetic progression (A.P.) starts with 2 and has a common difference of 3. To find the number of terms, we can use the formula for the nth term of an A.P., which is given by: nth term = a + (n-1)d, where a is the first term and d is the common difference. In this case, a = 2 and d = 3. We need to find the value of n when the nth term is 59. Plugging in these values into the formula, we get: 59 = 2 + (n-1)3. Simplifying this equation, we get: 57 = (n-1)3. Dividing both sides by 3, we get: 19 = n-1. Adding 1 to both sides, we get: 20 = n. Therefore, the number of terms in the A.P. is 20.

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6

3.

The first positive term of the A.P. -11, -8, -5,…..,

-4
3
-2
1

Correct Answer

A. 1

Explanation

The given arithmetic progression (A.P.) starts with -11 and has a common difference of 3. To find the first positive term, we need to find the first term in the A.P. that is greater than 0. Starting from -11, the next term is -8, then -5, and so on. The first positive term is 1, which is greater than 0. Therefore, the answer is 1.

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24

4.

Which of the following is not an A.P.?

-5, -2, 1, 4
11, 14, 17, 20
1, 4, 7
3, 7, 12, 18

Correct Answer

A. 3, 7, 12, 18

5.

The sum of first 20 odd natural number is

400
285
421
281

Correct Answer

A. 400

Explanation

The sum of the first 20 odd natural numbers can be calculated by using the formula n^2, where n is the number of terms. In this case, n is 20. So, the sum would be 20^2 = 400.

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6

6.

The sum of first 20 natural numbers is

210
190
170
110

Correct Answer

A. 210

Explanation

The sum of the first 20 natural numbers can be calculated using the formula for the sum of an arithmetic series. The formula is given by (n/2)(a + l), where n is the number of terms, a is the first term, and l is the last term. In this case, the first term is 1 and the last term is 20. Plugging these values into the formula gives (20/2)(1 + 20) = 10(21) = 210. Therefore, the correct answer is 210.

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5

7.

The sum of first 10 multiples of 7 is

385
406
315
371

Correct Answer

A. 385

Explanation

The sum of the first 10 multiples of 7 can be calculated by multiplying 7 by each of the numbers from 1 to 10 and then adding them together. In this case, the sum would be 7 + 14 + 21 + 28 + 35 + 42 + 49 + 56 + 63 + 70 = 385.

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3

8.

If the sum of the A.P. 3, 7, 11,………. is 210, the number is terms is

12
22
15
10

Correct Answer

A. 10

Explanation

The given arithmetic progression (A.P.) starts with 3 and has a common difference of 4. To find the number of terms, we can use the formula for the sum of an A.P., which is Sn = (n/2)(2a + (n-1)d), where Sn is the sum, n is the number of terms, a is the first term, and d is the common difference. Plugging in the values, we have 210 = (n/2)(2(3) + (n-1)(4)). Simplifying this equation gives 210 = (n/2)(6 + 4n - 4). Further simplification gives 210 = (n/2)(4n + 2). Solving for n, we get n = 10. Therefore, the number of terms is 10.

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7

9.

The 4th term from the end of the A.P ….., 2, 5, 8,….., 35 is

20
29
44
26

Correct Answer

A. 26

Explanation

The given arithmetic progression (A.P.) is: 2, 5, 8, ..., 35
The common difference (d) between consecutive terms is 5 - 2 = 3.
Now, we want to find the 4th term from the end. To do this, we'll work backward from the last term (35).
The last term (n) is 35. We want to find the 4th term from the end, so we'll subtract 3 times the common difference from 35, because there are 4 terms between the last term and the term we're looking for.
n = 35 - 3 * 3 n = 35 - 9 n = 26
So, the 4th term from the end of the A.P. is indeed 26.

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21

10.

The 11th and 13th terms of an A.P. are 35 and 41 respectively its common difference is

6
3
38
32

Correct Answer

A. 3

Explanation

In an arithmetic progression (A.P.), each term is found by adding a constant value (the common difference) to the previous term.
1. Set up the equations:
Let 'a' be the first term of the A.P.
Let 'd' be the common difference.
The general formula for the nth term of an A.P. is: a + (n-1)d
11th term: a + 10d = 35
13th term: a + 12d = 41
2. Solve for 'd':
Subtract the equation for the 11th term from the equation for the 13th term:
(a + 12d) - (a + 10d) = 41 - 35 2d = 6 d = 3
Therefore, the common difference is 3.

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15

11.

The next term of the A.P. ………. is

Correct Answer

A.

Explanation

To find the next term in the arithmetic progression (A.P.) represented by the sequence of square roots, you need to identify the common difference between consecutive terms.
Let's first calculate the common difference (d) for this sequence:
The first term: √8
The second term: √18
To find the common difference, subtract the first term from the second term:
Common Difference (d) = √18 - √8
Now, simplify:
d = √(9 * 2) - √(4 * 2)
d = (3√2) - (2√2)
d = √2
Now that we have the common difference (d = √2), we can find the next term in the sequence:
The third term: √32
To find the next term:
The fourth term = (third term) + (common difference) = √32 + √2 = 4√2 + √2 = 5√2
So, the next term in the sequence is 5√2.

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10

12.

If the sum of a₁ + a₁₀ = 50 for an A.P. Find the value of a₁ + a₂ +…… + a₁₀?

150
200
250
300

Correct Answer

A. 250

Explanation

The sum of the first and the tenth term of an arithmetic progression (A.P.) is given as 50. In an A.P., the sum of the terms can be found by using the formula: n/2 * (2a + (n-1)d), where n is the number of terms, a is the first term, and d is the common difference. Here, we have n = 10 (as we need to find the sum of the first 10 terms), and a1 + a10 = 50. Plugging these values into the formula, we get: 10/2 * (2a + 9d) = 50. Simplifying this equation gives us 5(2a + 9d) = 50, which further simplifies to 2a + 9d = 10. Since we need to find the sum of the first 10 terms, we can use the formula: S10 = 10/2 * (2a + (10-1)d) = 5(2a + 9d) = 5 * 10 = 50. Therefore, the value of a1 + a2 + ... + a10 is 250.

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2

13.

What would be the first negative term for an A. P. 121, 117, 113…..?

31
30
33
32

Correct Answer

A. 32

14.

The multiples of 4 that between 10 and 250?

51
60
71
81

Correct Answer

A. 60

Explanation

To find the multiples of 4 between 10 and 250, you can start by dividing 10 by 4 to find the first multiple, and then continue with increments of 4 until you reach 250. Here are the multiples of 4 in that range:
12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100, 104, 108, 112, 116, 120, 124, 128, 132, 136, 140, 144, 148, 152, 156, 160, 164, 168, 172, 176, 180, 184, 188, 192, 196, 200, 204, 208, 212, 216, 220, 224, 228, 232, 236, 240, 244, 248

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3

15.

For an A.P. 9, 17, 25….the number terms in order to give a sum of 636 is:

12
11
10
13

Correct Answer

A. 12

Explanation

The given sequence is an arithmetic progression with a common difference of 8. To find the number of terms required to give a sum of 636, we can use the formula for the sum of an arithmetic progression: Sn = (n/2)(2a + (n-1)d), where Sn is the sum, n is the number of terms, a is the first term, and d is the common difference. Plugging in the values, we have 636 = (n/2)(2*9 + (n-1)*8). Simplifying the equation, we get 636 = (n/2)(26 + 8n - 8). Solving for n, we find that n = 12. Therefore, the number of terms required to give a sum of 636 is 12.

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4

The Arithmetic Progression Test! Math Quiz

The common difference of the A.P. whose general term a_n = 2n + 1 is

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The number of terms in the A.P. 2, 5, 8,….., 59 is