Arithmetic Series (unknown term number)

If you are trying to determine how many terms are in a sequence, what formula do you need to use to find n?

What term number is 47 in the sequence? (n=?)

3, 7, 11, ..., 47

(a)  

How many terms are in the sequence?

4+11+18+...+39

What term number (n=?) is 39 in the sequence?

9+14+19+...+39

(a)  

Find S_n

8+17+26+...+125

A stadium has 100 seats in the first ring, 120 seats on the second ring, and 140 seats on the third ring. If the last ring around the stadium has 580 seats, how many seats are there in total in the stadium?

A hotel in Las Vegas has 100 rooms on the first floor, 84 rooms on the second floor, 68 rooms on the third floor and 4 rooms on the last floor. How many FLOORS are there?

A hotel in Las Vegas has 100 rooms on the first floor, 84 rooms on the second floor, 68 rooms on the third floor and 4 rooms on the last floor. How many ROOMS are there?