Question

The sum of first 16 terms of so is 112 and sum of its next 14 terms is 518.find ap

Answer 1

S16 =112
= n/2 {2a+(n-1)d}
= 16/2 {2a+15d}=112
= 8{2a+15d}=112
= {2a+15d}=14 ........(1)
Also the sum of next 14 terms is 518.
Now,
S30=S16+518
S30=112+518
S30=630
= 30/2 {2a+29d}=630
= 15 {2a+29d}=630
= {2a+29d}=42.........(2)
Solving the equations (1) &(2)...
We get,
d=2...
d in equ. (1)...
2a+15(2)=14
2a+30=14
2a=14-30
2a=-16
a=-8...
Therefore the required arithmetic series is...
a,a+d,a+2d,a+3d,...
= -8,-8+2,-8+2(2),-8+3(2),...
= -8,-6,-4,-2,.....