Background info:

if the terms of an arithmetic progression are a_1, a_2, a_3, ..., a_n, then the formula for an arithmetic progression is of the form:

where a_n is the nth term of the sequence, a_1 is the first term, n is the current number of the term and d is the common difference.

example, we may write the fifth term as:

a_5 = a_1 + (5 - 1)d = a_1 + 4d

the sum of the first n terms is given by the formula:

and we can express the sum of the first n terms in sigma notation by the following form:

So the above is just stuff you have to memorize at this point. if you decide to go to higher mathematics you can find out what all this stuff really means. you may see Arithmetic progression for more info

now on to your questions, i have attached them in a diagram below.

EDIT: the last formula should be SUM{n=0 to n=19}13 + 7n, that is plug in the value of d