Question

the 10th term of an A.P.is 52 and 16th term is 82.find the 32th term.

Answer 1

10th term of an A.P = 52
⇒ a + 9 d = 52 ---- 1
16th term of A.P = 82
⇒ a + 15 d = 82 ----- 2
On subtracting 2 from 1
a + 15 d = 82
-a - 9 d = -52
⇒ 6 d = 30
⇒ d = 5
a + 15(5) = 82
a = 82 - 75
a = 7
Therefore 32 th term of A.P = a + 31 d = 7 + 31(5) = 162
162 is the 32 th term

Answer 2

10th term=a+9d=52
16th term=a+15d=82
a+9d=52
a+15d=82
=6d=30
d=30÷6
d=5
substitute d=5 in equ 1
a+9(5)=52
a+45=52
a=52-45
a=7
32nd term=
a+31d
7+31(5)
7+155
=162