MATH HELP! [Arithmetic Sequences] 10th Grade.

1. Consider the arithmetic series 2 + 5 + 8 +...
a) Find an expression for Sn, the sum of the first n terms.
b) Find the value of n for which Sn= 1365.


2. An arithmetic sequence has 5 and 13 as its first two terms respectively.
a) Write down, in terms of n, an expression for the nth term, A(n).

(n) as in beneath the A like a power, only it's not.

b) Find the number of terms of the sequence which are less than 400.


3. Arturo goes swimming every week. He swims 200 metres in the first week. Each week he swims 30 metres more than the previous week. He continues for one year. (52 weeks)
a) How far does Arturo swim in the final week?
b) How far does he swim altogether?

CAN YOU EXPLAIN/HOW/ TO DO IT TOO? I want to learn, haha.
Thanks in advance!