Question

The sum $S_n$ of the terms of an arithmetic progression is defined by the formula $S_n=4n^2-3n$ for any $n$. Write the first three terms of the progression.

Answer 1

$S_n$ is the sum of $AP,S_n={4n}^2-3n$

Let first term$=a$ and common difference$=d$

So,$S_1=4{\left(1\right)}^2-3\left(1\right)=aa=1S_2=a+a+d=4{\left(2\right)}^2-3\left(2\right)\Rightarrow 2a+d=16-6\Rightarrow d=10-2=8$

The first three terms are,

$a,a+d,a+2d1,1+8,1+2\left(8\right)1,9,17$