Common Difference

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

$a_{21}-a_7=84$ ?

Q.

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

A. $\frac{n^2(n+1)}{6}$

B. $\frac{n(n+1)(n-1)}{6}$

C. $\frac{n(2n+1)}{6}$

D. $\frac{n(n+1)(2n+1)}{6}$

Q.

Write the $n^{th}$ term of odd numbers.

Q.

The angles of a quadrilateral are in A. P. with common difference ${20}^{\circ }$. Find its angles.

Q.

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

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Q. In an AP, it is given that S₅ + S₇ = 167 and S₁₀ = 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 $5n^2+4n.$ Find its $8^{th}$ 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 $AP:\sqrt{8},\sqrt{18},\sqrt{32},....$

Q.

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

Q.

Show that $(a-b{)}^2,(a^2+b^2)$ 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

1. $\frac{1}{41}$

2. $\frac{1}{45}$

3. $\frac{1}{37}$

4. $\frac{1}{49}$

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

1. $k^{n-1}\mathrm{adj}\left(A\right)$
2. $k^n\mathrm{adj}\left(A\right)$
3. $k^{n-2}\mathrm{adj}\left(A\right)$

Q.

For AP show that $a_p+a_{p+2q}=2a_{p+q}$

Q. Question 8
Solve the equation -4 + (-1) + 2 + . . . . . + x = 437.

Q.

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

1. A.P

2. G.P

3. H.P

4. 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

1. $24$ min

2. $34$ min

3. $125$ min

4. $135$ min

Q. Question 8
Which term of an AP : 21, 42, 63, 84, …. is 210?

A) $9^{th}$
B) ${10}^{th}$
C) ${11}^{th}$
D) ${12}^{th}$

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.