# Common Difference

## Trending Questions

**Q.**Which term of the AP 21, 18, 15, ... is −81?

**Q.**

In a given AP if pth term is q and qth term is p then show that it's nth term is (p+q-n)

**Q.**What is the common difference of an A.P. in which

a21−a7=84 ?

**Q.**

Find the sum of the squares of the first n natural numbers.

A. n2(n+1)6

B. n(n+1)(n−1)6

C. n(2n+1)6

D. n(n+1)(2n+1)6

**Q.**

Write the nth term of odd numbers.

**Q.**

The angles of a quadrilateral are in A. P. with common difference 20∘. Find its angles.

**Q.**

If 2x, x + 10, 3x + 2 are in AP. Find the value of x.

**Q.**In an AP, it is given that S

_{5 }+ S

_{7}= 167 and S

_{10 }= 235, then find the AP, where S

_{n}denotes the sum of its first n terms. [CBSE 2015]

_{ }

**Q.**

For what value of $k$ will $k+9$, $2k-1$ and $2k+7$ be the consecutive terms of an A.P?

**Q.**

The sum of n natural numbers is 5n2+4n. Find its 8th term.

**Q.**For what value of p, are 2p+1, 13, 5p-3 three consecutive terms of an AP?

**Q.**

What is the formula of the sum ${S}_{n}$ of the terms of an arithmetic progression.

**Q.**

Write the next term of the AP:√8, √18, √32, ....

**Q.**

The nth term of an AP is (3n + 5). Find its common difference.

**Q.**

Show that (a−b)2, (a2+b2) and (a+b)2 are in A.P.

**Q.**

The sum of three consecutive terms of an A. P. is 21 and the sum of their squares is 165. Find these terms.

**Q.**The common difference of an A.P., the sum of whose n terms is S

_{n}, is

(a) S

_{n}− 2S

_{n−1}

_{ }+ S

_{n−2}

(b) S

_{n}− 2S

_{n−1}

_{ }− S

_{n−2}

(c) S

_{n}− S

_{n−2}

(d) S

_{n}− S

_{n−1}

**Q.**

If the ${7}^{th}$ term of HP is $\frac{1}{10}$ and the ${12}^{th}$ term is $\frac{1}{25}$, then the ${20}^{th}$ term is

$\frac{1}{41}$

$\frac{1}{45}$

$\frac{1}{37}$

$\frac{1}{49}$

**Q.**A is a matrix of order n and k is a constant, then adj(kA) is

- kn−1adj(A)
- knadj(A)
- kn−2adj(A)

**Q.**

For AP show that ap+ap+2q=2ap+q

**Q.**Question 8

Solve the equation -4 + (-1) + 2 + . . . . . + x = 437.

**Q.**

The numbers $\sqrt{2}+1,1,\sqrt{2}-1$ will be in

A.P

G.P

H.P

None of these

**Q.**

A person is to count $4500$ currency notes. Let an denote the number of notes he counts in the nth minute. If $a1=a2=...=a10=150anda10,a11,....$are in AP with common difference $-2$ , then the time taken by him to count all notes, is

$24$ min

$34$ min

$125$ min

$135$ min

**Q.**

**Question 8**

Which term of an AP : 21, 42, 63, 84, …. is 210?

A) 9th

B) 10th

C) 11th

D) 12th

**Q.**The 9th term of an AP is −32 and the sum of its 11th and 13th terms is −94. Find the common difference of the AP. [CBSE 2015]

**Q.**In an AP the first term is 2, the last term is 29 and sum of all the terms is 155. Find the common difference of the AP.

**Q.**

IF (2p-1), 7, 3p are in AP, find hte value of p.

**Q.**

Find the value of p for which the numbers 2p-1, 3p+1, 11 are in AP.

Hence, find the numbers.

**Q.**Question 3

The list of numbers -10, -6, -2, 2, ... is

A) an AP with d = - 16

B) anAP with d = 4

C) an AP with d = - 4

D) not an AP

**Q.**

The 4th term of an AP is 11. the sum of the 5th and 7th terms of this AP is 34. Find its common difference.