Question

the 10th term of an a.p. is 52,and 16th term is 82 find the 32nd term

Answer 1

your ans is here

hope it helps!

Answer 2

Here is your solution

10th term of an a.p. is 52

a+9d = 52............... (1)

16th term of a.p. is 82

a+15d= 82.....................(2)

On subtracting equation (1) from (2)

$a+15d - (a+9d) = 82- 52 \\ \cancel a+15d - \cancel a - 9d = 30 \\ 6d = 30 \\ d = 5$
Putting value of d in equation (1)

a +9d = 52
a + 9×5=52
a+45=52
a=52-45
a= 7

32nd term= a + 31d
=>7+31×5
=>7+155
=>162

Hence,

32nd term = 162