Question

Sum of first 4 terms of an ap is 28 and first 8 terms is 88, find the sum of first 16 terms of that ap.

Answer 1

Answer:

304 is the sum of first 16 terms

Step-by-step explanation:

sum of first 4 terms = 28

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

S4 = 4/2 (2a + 3d) = 28

2 (2a + 3d) = 28

2a + 3d = 28/2 = 14 equ (1)

S8 = 8/2 ( 2a + 7d) = 88

4(2a + 7d) = 88

2a + 7d = 88/4 = 22 equ (2)

subtract equ (2) - (1)

2a + 7d = 22

2a + 3d = 14

4d = 8

d = 8/4 = 2

substitute d = 2 in equ (1)

2a + 3d = 14

2a + 3(2) = 14

2a + 6 = 14

2a = 14 - 6

2a = 8

a = 8/2 = 4

a = 4 d = 2

S16 = 16/2 (2(4) + (16-1)2)

= 8 ( 8 + 30)

= 8 × 38

= 304

hope you get your answer