Can someone help me with arithmetic progressions?

Question

i need help understanding the terms and formulas of arithmetic progresions in general, my teacher kind of wizzed through it in class and i don't really understand. I'd like to know when to use certain formulas i'd like to see how they are written out like in words too,
for example when i heard the gauss theory and how he thought of it it really helped. Here are two example questions:

1. Find the sum of all the multiples of three between 1 and 100 and
2. Given that 5 +9+13 +17+...+Un= 2414, find n and Un

I think i found the first one ( i got 5049) but i'm really not sure, and the second one i don't know which formula to use.

Answer 1

For arithmetic progressions, the difference between consequtive terms is a constant.

for
1) each will differ by 3
2) each differs by 4,

the general form is a0 + (k-1)*d where d is the difference.

Btw, for geometric progressions, it's the ratio between terms that's constant, not the difference.