Question

The sum of first 8 terms of an AP is 100 and sum of first 19 terms is 551. Find AP.

Answer 1

use of formula ap

we know that n

so find ap

Answer 2

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=(38a+342d)

1102=2(19a+171d)

1102/2=19(a+9d)

551/19=a+9d

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

25=2a+7d......×1

29=a+9d.....×2

25=2a+7d

58=2a+18d

eq 2-1

33=11d

33/11=d

d=3

substitute d=3 in eq 1

25=2a+7×3

25=2a+21

25-21=2a

4=2a

a=4/2

a=2

So the AP is 2,5,8,11......