How many terms (summands) are in the sum? I realize there are similar stacks to my question such as:
How many summands are there
Although I require further clarifications to understand.

Consider the sequence: 4 + 11 + 18 + 25 + ... + 249.

1) How many summands are in the sum.
2) Compute the sum.

By simple investigation, you can observe that the sequence you're dealing with is an arithmetic progression, hence if you name it $a_n$, then you're interested in summing the sequence $a_n$ defined by:
$$
a_n=4+7n, n\in\mathbb N
$$
And to know how many summands there are, yoi solve for $n$ such that:
$$
a_n=249=4+7n
$$
Hence $n=35$, so there are $36$ summands.
The sum is simply:
$$
a_0+a_1+...a_{35}=\sum_{n=0}^{35}4+7n=4\times 36+7\times\frac{35\times 36}{2}=4554
$$
