Answer
Arithmetic
Sum: $2n^2-2n$
Work Step by Step
We are given the sequence:
$0.4,8,12,.....$
We determine the difference between consecutive terms:
$4-0=8-4=12-8=4$
As the difference between consecutive terms is constant, the sequence is arithmetic. Its elements are:
$a_1=0$
$d=4$
Determine the sum of the first $n$ terms:
$S_n=\dfrac{n(2a_1+(n-1)d)}{2}=\dfrac{n(2(0)+(n-1)(4))}{2}=\dfrac{4n(n-1)}{2}=2n(n-1)=2n^2-2n$
