Question

If the sum of n terms of an AP is
$3n {2} + 1$
then the first term is ....​

Answer 1

Step-by-step explanation:

$\\ \tt\hookrightarrow S_n=3n^2+1$

$\\ \tt\hookrightarrow S_{n-1}=3(n-1)^2+1$

$\\ \tt\hookrightarrow S_{n-1}=3(n^2-2n+1)+1$

$\\ \tt\hookrightarrow S_{n-1}=3n^2-6n+3+1$

$\\ \tt\hookrightarrow S_{n-1}=3n^2-6n+4$

Now

$\\ \tt\hookrightarrow t_n=S_n-S_{n-1}$

$\\ \tt\hookrightarrow<strong> </strong>3n^2+1-(3n^2-6n+4)$

$\\ \tt\hookrightarrow 3n^2+1-3n^2+6n-4$

$\\ \tt\hookrightarrow 6n-3$

So

$\\ \tt\hookrightarrow t_1=6(1)-3$

$\\ \tt\hookrightarrow 6-3$

$\\ \tt\hookrightarrow 3$