Answer
$2n^2-3n$
Work Step by Step
We have to determine the sum:
$S=-1+3+7+.....+(4n-5)$
As $3-(-1)=7-3=...=4$, the sequence is arithmetic.
Determine its first term and the common difference:
$a_1=-1$
$d=4$
The given sum contains $n$ terms; therefore we have to determine the sum of the first $n$ terms. We use the formula:
$S_n=\dfrac{n(a_1+a_n)}{2}$
$-1+3+7+...+(4n-5)=\dfrac{n(-1+4n-5)}{2}$
$=\dfrac{n(4n-6)}{2}$
$=n(2n-3)$
$=2n^2-3n$
