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

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

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:
[tex]a_n=1+3(n-1)[/tex]

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