Question

if the sum of n terms of an AP is 3 n^2 + n and the common difference is 6 , then find its first term .

Answer 1

Answer:

first term of an A.P is 4.

Step-by-step explanation:

Hi,

Given that Sum to n terms of an AP is

3n² + n

Given common difference is 6,

If suppose a is the first term of A.P and 'd' is the

common difference, the Sum to n terms of an A.P is

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

Given Sn = 3n² + n

If we substitute n = 1 , in Sn we get Sum to 1 tems of an A.P

which is equivalent to first term of A.P itself,

So, 1st term of A,P = S₁ = 3.1² + 1

= 3 + 1

= 4.

Hence, first term of an A.P is 4.

Hope, it helps !

Answer 2

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

3n^2+n =n/2[2a+(n-1)6]

=> n(3n+1)=n/2[2a+6n-6]

=> 6n+2 =2a +6n-6

=> 8=2a => 2a=8 => a=4

Therefore 1st term is 4