Question

Express the following sum in sigma notation: 1+4+7+10+13

Answer 1

The sum would be written as:
$\Sigma_{n=1}^{5} (3n-2)$

It goes from n=1 to =5 because it is the first 5 terms of the sum.
The sequence has a first term, a₁, of 1.  The common difference, d, is 3.  The explicit formula would then be:
$a_n=1+3(n-1)$

Using the distributive property to simplify, we would have:
$a_n=1+3n-3 \\a_n=3n-2$