Question

Onsider the arithmetic series: 1 + 9 + 17 + 25 + ... write a formula for the sum of the first n terms in this series.

Answer 1

We can see this is a summation of multiples of 8 plus 1, which starts at 1.

This can be written in the following way:

`\Sigma_(m=0)^(n)(8m+1)`

Lets verify the summation expression by doing the sequence for the first 4 elements (hence
`n=3`, as it starts from 0):

`\Sigma_(m=0)^(3)(8m+1)=[8(0)+1]+[8(1)+1]+[8(2)+1]+[8(3)+1]=`

`1+9+17+25`

As you can see, the generalization is correct.