Question

the sum of first eight terms of an AP is 100 and the sum of first nineteen terms is 551 .Find AP

Answer 1

Sum of first 8 terms =8a+28d=100
Sum of first 19 terms=19a+171d=551
Simplify
a+9d=29
2a+7d=25
On solving we get a=2 d=3

Answer 2

HERE IS YOUR ANSWER;

Sn=n/2[2a+(n-1)d] Is the sum of the n terms.

NOW FOR THE EIGHTH TERM;

S8= 8/2[2a+(8-1)d]

S8=8a+28d=100
2a+7d=25 ......1)

Now,

Similar for 19th term;

s19=a+9d=29......2)

Now using elimination method;

a=2 and d=3

HOPE it helps