Question

the tenth term of an A.P is 52 and 16th term is 82 find the 32nd term and general term

Answer 1

given,

10th term=52
a+9d=52---(1)

16th term =82
a+15d=82---(2)

(2)-(1)=
a+15d-a-9d=82-52
6d=30
d=5---(3)

substitute (3) in (1)
a+9d=52
a+45=52
a=7

a32=a+31d
=7+31*5
=7+155
=162

general term=a+(n-1)d
                      = 7+(n-1)5
                      =7+5n-5
                      = 5n+2

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