Question

The third term of an arithmetic series is -10 and the sum of the first eight terms of the series is 16.
Find the first term and common difference.

Answer 1

Answer:

Step-by-step explanation: a3=-10

And S8=16

Then ,

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

16=1/8(2a+7d)

16*8=2a+7d

128=2a+7d

a=(128-7d)/2........(1)

And

a3=a+2d

-10=a+2d

a=-2d-10.......(2)

And

From (1) and (2)

-2d-10=(128-7d)/2

-4d-20=128-7d

-4d+7d=128+20

3d=148

d=148/3

And a =-2(148/3)-10

a=(-296/3)-10

a=-108.66