Question

The sum of 8 terms of an A.P. is 64, and the sum of 17 terms is 289. Find the sum of its ‘n’ terms.

Answer 1

`S_n = n/2[2a + (n - 1)d]`

`S_8 = 8/2[2a + (8 - 1)d]`

64 = 4[2a + 7a]

16 = 2a + 7d

2a + 7d = 16    ...(1)

`S_17 = 17/2[2a + (17 - 1)d]`

289 = `17/2[2a + 16d]`

34 = 2a + 16d

2a + 16d = 34    ...(2)

Subtract (1) from equation (2)

2a + 16d = 34

 2a + 7d = 16
−    −     −      

         9d = 18

d = `18/9`

d = 2

Put the value d = 2 in equation 1.

2a + 7d = 16

2a + 7(2) = 16

2a + 14 = 16

2a = 16 − 14

2a = 2

a = `2/2`

a = 1

`S_n = n/2[2a + (n - 1)d]`

= `n/2[2(1) + (n - 1)2]`

= `(2n^2)/2`

S_n = n²