Question

Sum of first 4 terms of ap isv28 and first 8 terms is 88, find the sum of first 16 terms

Answer 1

Sum of first four terms = 28

S4 = 4/2 [2a + (4-1)d]
28 =2 [2a+ 3d]
14 = 2a+3d ____________{1}

Sum of eight terms = 88

S8 =8/2 [2a+(8-1)d]
88 =4 [2a+7d]
22 = 2a+7d __________{2}

By elimination method :-

2a + 3d = 14
2a + 7d = 22
- - -

-4d = -8
d=2

Using value of d in {1}

2a+ 3(2)=14
2a=14-6
2a= 8
a=4

S16 = 16/2 [2(4) + (16-1) (2) ]
= 8 [8+34]
= 8 [42]
= 336