As a shortcut for writing out long sums, we can use the symbol  ∑ ​ with the following "settings":

Here k is called the index, but it is not always k.

Example

Write the sum 2+5+8+⋯+38 in  ∑ ​ form.

We recognize an arithmetic sequence with u1​=2 and d=3, so un​=2+3(n−1)=3n−1. Then we can write the sum

All that remains is to find the "end value" of n, which in this case is the n that makes un​=38:

So the sum is