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The common difference of the AP (1)/(p),...

The common difference of the AP `(1)/(p), (1-p)/(p), (1-2p)/(p)`,…. Is

A

`p`

B

`-p`

C

`-1`

D

`1`

Text Solution

Verified by Experts

The correct Answer is:
C
`d = {(1-p)/(p) - (1)/(p)} = ((1-p-1)/(p)) = (-p)/(p) = -1.`
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Assertion (A) : Common difference of the A.P.: -5,-1,3,7, ……. Is 4. Reason (R ) : Common difference of the A.P.a,a+d, a+2d , …., is given by d =2^(nd) term -1^(st) term.

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Knowledge Check

  • Common difference of the A.P. -5, -1, 3, 7, …… is :

    A
    `-4`
    B
    `2`
    C
    `4`
    D
    `-5`

  • If p is positive, then the sum to infinity of the series, 1/(1+p) -(1-p)/(1+p)^2 + (1-p)^2/ (1+p)^3 -........ is

    A
    `1//2`
    B
    `3//4`
    C
    `1`
    D
    None of these

  • Assertion (A) : Common difference of the A.P.: -5,-1,3,7, ……. Is 4. Reason (R ) : Common difference of the A.P.a,a+d, a+2d , …., is given by d =2^(nd) term -1^(st) term.

    A
    Both A and R are true and R is the correct explanation for A.
    B
    Both A and R are true and R is not correct explanation for A.
    C
    A is true but R is false.
    D
    A is false but R is true.
    • RS AGGARWAL-ARITHMETIC PROGRESSION-Multiple Choice Questions (Mcq)
    1. The common difference of the AP (1)/(p), (1-p)/(p), (1-2p)/(p),…. Is

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    2. The common difference of the AP (1)/(3), (1-3b)/(3), (1-6b)/(3),… is

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    3. The next term of the AP sqrt(7), sqrt(28), sqrt(63),… is

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    4. If 4, x(1), x(2), x(3), 28 are in AP then x(3) = ?

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    5. If the nth term of an AP is (2n +1) then the sum of its first three te...

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    6. The sum of first n terms of an AP is (3n^(2) + 6n). The common differe...

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    7. The sum of first n terms of an AP is (5n - n^(2)). The nth term of the...

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    8. The sum of the first n terms of an A.P. is 4n^2+2n . Find the n ...

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    9. The 7th term of an AP is -1 and its 16th term is 17. The nth term of t...

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    10. The 5th term of an AP is -3 and its common difference is -4. The sum o...

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    11. The 5th term of an AP is 20 and the sum of its 7th and 11th terms is 6...

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    12. The 13^(th) term of an AP is 4 times its 3^(rd) term. If its 5^(th) te...

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    13. An AP 5, 12, 19, … has 50 terms. Its last term is

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    14. The sum of first 20 odd natural numbers is

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    15. The sum of first 40 positive integers divisible by 6 is

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    16. How many two -digit numbers are divisible by 3?

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    17. How many three-digit numbers are divisible by 9?

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    18. What is the common difference of an AP in which a(18)-a(14) = 32?

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    19. If a(n) denotes the nth term of the AP 3, 18, 13, 18,… then what is th...

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    20. Which term of the AP 72, 63, 54, … is 0?

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