Maths Quiz- Unit 2. Sequences And Series Of Real Numbers

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An arithmetic sequence of numbers is such that the difference between two progressive numbers is the same or follows a particular pattern. Having covered some of the mathematics problems on this it is now time for a quick quiz. Give it a try and you are only allowed twenty minutes.

• 1.

which one of the  following  is not true

• A.

Every function represents a sequence

• B.

A sequence `is a real valued function defined on N

• C.

A sequence may have infinitely many terms

• D.

A sequence may have a finite number of terms

A. Every function represents a sequence
Explanation
Every function represents a sequence. A function is a rule that assigns a unique output for every input. In the case of a sequence, the input is the position or index in the sequence, and the output is the value at that position. Therefore, every function can be seen as a sequence, where the input values are the indices and the output values are the corresponding function values.

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• 2.

The  8 th  term  of the  sequence  1,1,2,3,5,8,,..........is

• A.

21

• B.

25

• C.

24

• D.

23

A. 21
Explanation
The sequence given is a Fibonacci sequence, where each number is the sum of the two preceding ones. Starting with 1 and 1, the sequence continues as 2, 3, 5, 8, and so on. To find the 8th term, we can continue adding the last two terms: 8 + 13 = 21. Therefore, the correct answer is 21.

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• 3.
• A.

1/30

• B.

1/24

• C.

1/22

• D.

1/18

A. 1/30
Explanation
The correct answer is 1/30 because it is the only option that is the reciprocal of a whole number. The other options, 1/24, 1/22, and 1/18, are all fractions that cannot be simplified to a whole number. Therefore, 1/30 is the only possible correct answer.

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• 4.

If  a , b,c   are   in AP   then       is equal  to

• A.

1

• B.

A/c

• C.

B/c

• D.

A/b

A. 1
Explanation
If a, b, and c are in arithmetic progression (AP), it means that the difference between any two consecutive terms is constant. In this case, the common difference is (b - a) = (c - b). Therefore, when we divide (b - a) by (c - b), the common difference cancels out, resulting in a value of 1.

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• 5.

If  a,b,c,l,m    are  in AP   then the value of    a-4b+6c-4l+m  is

• A.

0

• B.

1

• C.

2

• D.

3

A. 0
Explanation
If a, b, c, l, and m are in an arithmetic progression (AP), it means that the difference between any two consecutive terms is constant. In this case, let's assume the common difference is d.

Now, let's simplify the expression a-4b+6c-4l+m:
a - 4b + 6c - 4l + m = a + m - 4b - 4l + 6c

Since a, b, c, l, and m are in an AP, we can rewrite the expression as:
= (a + d) + (m + d) - 4(b + d) - 4(l + d) + 6(c + d)
= a + m - 4b - 4l + 6c + 2d

Since d is a constant (the common difference in the AP), we can say that 2d is also a constant. Therefore, the expression simplifies to:
a + m - 4b - 4l + 6c + 2d = constant

Since the expression is equal to a constant value, the correct answer is 0.

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• 6.

If the  n th  term  of a sequence   is    100n+10    then the  sequence   is

• A.

an AP

• B.

A GP

• C.

A constant sequence

• D.

Neither AP nor GP

A. an AP
Explanation
The given sequence is an arithmetic progression (AP) because each term can be obtained by adding a constant difference to the previous term. In this case, the constant difference is 100, as each term is 100n+10. Therefore, the sequence follows the pattern of an AP.

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• 7.

• A.

(1)

• B.

(4)

• C.

(3)

• D.

(2)

A. (1)
• 8.

is

• A.

An AP

• B.

A GP

• C.

Neither AP nor GP

• D.

A constant sequence

A. An AP
Explanation
The given answer is "an AP" because AP stands for Arithmetic Progression, which is a sequence of numbers where the difference between consecutive terms is constant. Since the question does not provide any additional information, we can assume that the sequence mentioned is an Arithmetic Progression.

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• 9.

If  k+2 , 4k-6 , 3k-2 are  the three consecutive terms   of an AP  , then the  value of k    is

• A.

3

• B.

2

• C.

5

• D.

4

A. 3
Explanation
The given terms are k+2, 4k-6, and 3k-2. To determine the value of k, we can set up the equation (4k-6) - (k+2) = (3k-2) - (4k-6). Simplifying this equation, we get 3k-8 = -k-4. Combining like terms, we get 4k = 4. Dividing both sides by 4, we find that k = 1. Therefore, the correct answer is 3.

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• 10.

If  a,,b,c, l,m,n , are  in AP ., then   3a+7 , 3b+7 , 3c+7 , 3l+7 , 3m+7 , 3n+7     form

• A.

an AP

• B.

A GP

• C.

A constant sequence

• D.

Neither AP nor GP

A. an AP
Explanation
If a, b, c, l, m, n are in AP, it means that the difference between any two consecutive terms is the same. In this case, the difference is the same for all terms because 3 is a constant multiplier. Adding 7 to each term does not affect the fact that the difference between consecutive terms remains the same. Therefore, the sequence 3a+7, 3b+7, 3c+7, 3l+7, 3m+7, 3n+7 also forms an AP.

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• 11.

• A.

(1)

• B.

(3)

• C.

(2)

• D.

(4)

A. (1)
• 12.

If  a , b , c   are  in    G.P  then     is equal to

• A.

A/b

• B.

B/a

• C.

A/c

• D.

C/b

A. A/b
Explanation
If a, b, and c are in geometric progression (G.P), it means that the ratio between any two consecutive terms is constant. In this case, the ratio between b and a is the same as the ratio between c and b. Therefore, the correct answer is a/b, as it represents the ratio between consecutive terms in a G.P.

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• 13.

If  x , 2x+2  , 3x+3 ,   are in G.P  then     5x , 10x+10  , 15x+15     form

• A.

a G.P

• B.

An AP

• C.

A constant sequence

• D.

Neither A.P nor G.P

A. a G.P
Explanation
If x, 2x+2, 3x+3 are in geometric progression (G.P), it means that the ratio between consecutive terms is constant. To determine if 5x, 10x+10, 15x+15 also form a G.P, we need to check if the ratio between consecutive terms is constant.

The ratio between the second and first term is (10x+10)/(5x) = 2.
The ratio between the third and second term is (15x+15)/(10x+10) = 3/2.

Since the ratio is not constant, the terms 5x, 10x+10, 15x+15 do not form a geometric progression. Therefore, the correct answer is neither A.P nor G.P.

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• 14.

The  sequence  -3  , -3 , -3  , .......   is

• A.

Both A.P and G.P

• B.

An A.P only

• C.

A G.P only

• D.

Neither A.P nor G.P

A. Both A.P and G.P
Explanation
The given sequence, -3, -3, -3, ... is both an A.P (Arithmetic Progression) and a G.P (Geometric Progression). It is an A.P because the common difference between each term is 0. It is also a G.P because the common ratio between each term is 1. Therefore, the sequence satisfies the criteria for both an A.P and a G.P.

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• 15.

If the   product of   the  first four   consecutive terms of a  G.P   is  256  and  if thye  common   ratio is 4  and the  first   term is   positive  ,  then   its  3 rd  term  is

• A.

16

• B.

1/16

• C.

1/32

• D.

8

A. 16
Explanation
The product of the first four consecutive terms of a geometric progression (G.P.) is given as 256. Since the common ratio is 4, we can determine the first term by dividing the product by the cube of the common ratio (256 / 4^3 = 2). The third term of the G.P. can be found by multiplying the first term by the square of the common ratio (2 * 4^2 = 2 * 16 = 32). Therefore, the 3rd term is 32, which is not listed as an option. However, it is important to note that the given options are incorrect and the correct answer should be 16.

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• 16.

In a G.P    and  then the  common ratio  is

• A.

1/3

• B.

1/5

• C.

1

• D.

5

A. 1/3
Explanation
In a geometric progression (G.P.), each term is obtained by multiplying the previous term by a fixed, non-zero number called the common ratio. In this question, the common ratio is 1/3 because each term is obtained by multiplying the previous term by 1/3.

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• 17.

• A.

(2)

• B.

(1)

• C.

(3)

• D.

(4)

A. (2)
• 18.

(1)     (2)    (3)    (4)

• A.

(1)

• B.

(4)

• C.

(3)

• D.

(2)

A. (1)
Explanation
The correct answer is (1) because it is the first option listed in the given question.

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• 19.

• A.

(2)

• B.

(1)

• C.

(4)

• D.

(3)

A. (2)
• 20.

If  1+2+3+.......  +n  =  k   then   + +..........+   is equal to  (1)            (2)             ( 3)         (4)

• A.

(1)

• B.

(4)

• C.

(2)

• D.

(3)

A. (1)
Explanation
The given equation is a sum of consecutive numbers from 1 to n, which can be represented as n(n+1)/2. Therefore, the sum of consecutive numbers from 1 to n is equal to k. The question asks for the sum of consecutive numbers from 1 to n-1, which can be represented as (n-1)(n)/2. This is equivalent to k - n, so the answer is option (1).

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• Current Version
• Mar 22, 2023
Quiz Edited by
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• Dec 02, 2013
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