Question

for an AP the 10th term is 52 and the 16th term is 82. find the nth term and the 32nd term of the AP.

Answer 1

Here is your solution

Given :-

a10=52
I. e
a+9d=52............ (1)

a16=82
I. e
a+15d=82................. (1)


subtract equation (i) from (ii)

a+15d-(a+9d)=82-52
=>15d-9d=30
=>6d=30
=>d=5

put d = 5 in (i)
a+9d=52
a+9(5)=52
a=52-45
a=7

a32=a+31d
​a32=7+31(5)
a32=7+155=162

Hence,
32 term is 162

hope it helps you