Question

if the sum of n terms of an ap is n2+1 then its first term is

Answer 1

n th term l = 2n+1 (given)-----(1)

If we put n=1,we get first term of an A.P.

Then first term a=2(1)+1

a=3;-----(2)

Now we can find out sum of first n terms using this formula

sum of n terms of an A.P.=n/2(a+l)

(Here a is first term of an A.P. and l is last or nth term of A.P.)

Values of a and l putting in the equation (3) from (2) and (1)

Sum of first n terms of an A.P.=n/2(3+2n+1)

=> n/2(2n+4)

=> n(n+2)

Finally, sum of first n terms of an A.P. is n(n+2) Ans.

Answer 2

Answer : 2

Step-by-step explanation :

Sum of n terms of an A. P

$S_{n} = n^2+ 1 \:$

However, we know

$S_{1} = T_{1} \:$

So first term,

$\implies T_{1} \\ \implies \: S_{1} \\ \implies 1^2 + 1 \\ \implies 1 + 1 \\ \implies2$

Therefore the first term is 2.

Conceptual knowledge :
Arithmetic progression is a sequence in which there is a common difference between the terms.

In other words, Next term is found by adding or subtracting a specific number.

If a is the first term, and considering d as common difference

The AP thus formed would be a, a+d, a+2d, a+3d....

One relation that comes handy is, there's a common difference between terms.