Question

the 10th term of an ap is -37 and sum of its 1st 6 term is -27 . find the sum of 1st 8 term.

Answer 1

a10 = -37

-37 = a + 9d

-37-9d =a

s6 = -27

n/2 (2a +(n-1)d)=-27

6/2(2(-37-9d)+(6-1)d) =-27

3(-74-18d+5d)=-27

-74-13d = -9

74+13d=9

13d = 9-74
d = 65/13 = 5

a= -37-9d
= -37-45
= -82

s8 = n/2 ( 2a +(n-1)d)
= 8/2 ( -82*2+(8-1)5)
=4(-164+35)
=4*-129
= -516