Question

the 10th term of an ap is 52 under 16 term is 82 find the 32nd term and general form

Answer 1

a+15d=82
a+9d=52
...................
6d=30
d=5
a+9(5)=52
a+45=52
a=52-45
a=7,d=5
32 term= a+31d
7+31(5)
7+155
162 is answer

Answer 2

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