Sequences/series

given the 4th term of a sequence is 21 and the 7th term is 36 find the 10th term and the sum of the first 20 terms

Use the formula for arithmetic sequence for the 4th term and 7th term, solve simultaneously to find the value of the 1st term as well as the difference. Then just sub it in for the formula for the first 20th terms.

but how do you find (or what is) the arithmetic sequence for the terms?

You use the formula started in your textbook and taught in lessons (assuming that you aren't a private candidate):
$x_n = a+d(n-1)$.

Here a is the starting point, and d is the difference between each term. We use $(n-1)$ as d is not used in the first term.