Answer
Arithmetic;
Sum: $2n-4n^2$
Work Step by Step
We are given the sequence:
$-2,-10,-18,-26,....$
Determine the difference of consecutive terms:
$a_2-a_1=-10-(-2)=-8$
$a_3-a_2=-18-(-10)=-8$
$a_4-a_3=-26-(-18)=-8$
As the difference of consecutive terms is constant, the sequence is arithmetic. Its elements are:
$a_1=-2$
$d=-8$
Determine the sum of the first $n$ terms:
$S_n=\dfrac{n(2a_1+(n-1)d)}{2}$
$S_n=\dfrac{n(2(-2)+(n-1)(-8)}{2}=\dfrac{n(-4-8n+8)}{2}=\dfrac{n(4-8n)}{2}=2n(1-2n)=2n-4n^2$
