Arithmetic Progressions — Class 10 Mathematics (Standard) PYQs

In an A.P., if $a_{14}-a_8=24$, then the common difference of the A.P. is

(a) In an A.P., $15^{\text{th}}$ term exceeds the $8^{\text{th}}$ term by $21$. If sum of first $10$ terms is $55$, then form the A.P.
OR
(b) The sum of first $n$ terms of an A.P. is $2n^2+13n$. Find its $n^{\text{th}}$ term and hence $10^{\text{th}}$ term.

If $a_n$ represents $n^{\text{th}}$ term of the A.P. $\frac{15}{4},\frac{10}{4},\frac{5}{4},\dots$ then value of $a_{16}-a_{12}$ is

If the sum of first $m$ terms of an AP is $2m^2+3m$, then its second term is :

Case Study - 3

Three numbers in AP have the sum $30$. What is its middle term ?

The 11th and 13th term of an AP are $39$ and $45$, respectively. What is the common difference of the AP ?

The 10th term of the AP $5,\frac{19}{4},\frac{9}{2},\frac{17}{4},\dots$ is :

Assertion (A) : Common difference of the AP : $5,1,-3,-7,\dots$ is $4$.
Reason (R): Common difference of the AP : $a_1,a_2,a_3,\dots ,a_n$ is obtained by $d=a_n-a_{n-1}$.

A sum of ₹$2,000$ is invested at $7\%$ per annum simple interest. Calculate the interests at the end of 1st, 2nd and 3rd year. Do these interests form an AP ? If so, find the interest at the end of the 27th year.