# Thread: Progressions and finding the sum of terms

1. ## Progressions and finding the sum of terms

Given this series (2,4,6,8,10,12...) the formula to find the sum of all numbers up to an nth term in the series is n(n+1).

For example, the sum of numbers up to and including the 2nd term is 2(2+1)=6.

But for this series (3,6,9,12,15...) what is the formula to find the sum of all numbers up to the nth term in the series.

What type of progression is it?

How is the formula found?

2. Is an arithmetic progression.

$a_1=3, \ a_n=3n$

The sum is $S_n=\frac{(a_1+a_n)n}{2}=\frac{3n(n+1)}{2}$

3. Thanks for the help.