Question

if the sum of the first n terms of an ap is 3nsquare+1 and it's common difference is 6 then find the first term​

Answer 1

Answer:

use formula Sn= n/ 2 [2a +(n-1)d]

Answer 2

if the sum of the first n terms of an ap is 3nsquare+1 and it's common difference is 6 then the first term​ is a = (1+3n)/n

Given,

Sn = 3n² + 1

d =  6

a = ?

we use formula,

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

3n² + 1 = n/2 [ 2a + (n-1) 6 ]

3n² + 1 = n/2 [ 2a + 6n - 6 ]

3n² + 1 = n [ a + 3n - 3 ]

3n² + 1 = an + 3n² - 3n

1 = an  - 3n

1 + 3n =  an

a = (1+3n)/n