Question

The sum of first 8 terns of an AP is 100 and sum of first 19 terms is 551.find A.P​

Answer 1

S8=100

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

100=8/2(2a+(8-1)d)

100=4(2a+7d)

100/4=2a+7d

25=2a+7d.....eq 1

S19=551

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

551=19/2(2a+(19-1)d)

551×2=19(2a+18d)

1102/19=2(a+9d)

58/2=a+9d

29=a+9d.....eq 2

25=2a+7d....×1

29=a+9d......×2

25=2a+7d

58=2a+18d

eq 2- eq 1

58-25=18d-7d

33=11d

d=33/11

d=3

substitute d=3 in eq 1

2a+7×3=25

2a+21=25

2a=25-21

2a=4

a=4/2

a=2

So, the AP is 2,5,8.......

hope this answer helps you