Can you answer these math word problems and describe how you solved them?

Question

Find the sum of arithmetic series if a1=3 d=.5 an=7.5
How many terms in sequence -4,1,6,11,...,356
In arithmetic sequence S30=240 d=2 find a1
In arithmetic sequence a1=-6 S50=-5150 find a50

Answer 1

1. You have a sequence starting with 3. The next term is 3.5, each succeeding term is 0.5 larger than the one before it. The last term is 7.5
First you figure out HOW MANY terms you have. Thats 10. There is a formula to figure out the sum, which involves a1, d, and the number of terms, find it, substitute in your values and solve.
2. You have a sequence starting a -4, progressing 5 units to the next term, and so on, until you reach 356. Find the difference between the first and last term, (360) and divide that by the progression d (5) to get 72.
3. You have a sequence that has 30 terms. The sum of these is 240, and the progression d is 2 (even number counting). You have enough info to go into the sum formula to solve for a1.
4. You have a sequence that starts at -6 and each term is m units less than the previous. The sum of all terms from -6 to the last is -5150, and there are 50 terms in the sequence. You want to find the last. You can use the sum formula to solve for this, you may need to so some trial and error, but not too much.

Answer 2

Formulas are: .........................................................

3 + 3.5 + 4 + 4.5 + 5 + 5.5 + 6 + 6.5 + 7 + 7.5 = 52.5

d = +5, find out how many times you added d
going from -4 to 356 is a total of 356 - -4 = 360
360/5 = 72.. so there are 73 terms

a1= -6 S50 = -5150
a50 = ?

Use formula to