Question

What is the common difference if an arithmetic sequence sum of first 10 term is 250 and sum of first 16 terms is 592

Answer 1

Sn = n÷2( 2a+(n-1)d)

S10=10/2 ( 2a + 9d)

250=5(2a+9d)

10a + 45d = 250........(1)

S16= 16/2 (2a+15d)

592=8(2a+15d)

16a + 120d= 592.........(2)

Divide (1) by 5; we get

2a + 9d = 50 now multiply this by 8; we get

16a + 72d = 400 . Subtract this from (2)

Then d= 3