Question

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

Answer 1

Let a be first term and d be common difference
A/q
(8/2)[2a+(8-1)d] = 100
⇒2a + 7d =25_____(1)
and (19/2)[2a + (19-1)d] = 551
⇒2a + 18d = 58____(2)
subtracting equation (1) and (2)
11d = 33
⇒d = 3
so a = (25 - 21)/2 = 2
so AP = 2,5,8.11,14.......

Answer 2

And:

S8 = 100

S19= 551

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

S8=8/2{2a+(8-1)d}

100=4{2a+7d}

2a+7d=25

S19= 19/2 {2a+(19-1)d}

551×2/19=2a+18d

2a+18d=58

By Elimination Method

2a+18d=58

(-) 2a+ 7d=25

------------------------

11d=33

d=3

2a+7d= 25

2a+7(3)=25

2a=25-21

a=4/2

a = 2

AP = 2,5,8,11,14....…...