Question

The sum of the first nine terms of an arithmetic series is 135, and the first term is 17. Find the ninth term.

Answer 1

l = 13

Explanation:

given,

Sum of first 9 term = 135

first term (a) = 17

n = 9

l = a + (n -1)d

l = 17 + (9-1)d

l = 17 + 8 d

`S_n = (n)/(2)(a+l)`

`135 = (9)/(2)(17+17 + 8 d)`

`135 = {9}* (17+ 4 d)`

15 = 17 + 4 d

d = -0.5

now 9 th term

l = 17 + 8 d

l = 17 + 8 × (-0.5)

l = 13