How many terms are there in a geometric series if the first term is 5, the common ratio is 2, and the sum of the series is 315?

  6

Step-by-step explanation:

There are few enough that you can write the series and add them up. The first few terms are ...

  5, 10, 20, 40, 80, 160, 320

You know that 320 won't be part of the sum. Adding the first 6 terms gives 315, so there are 6 terms in the series.

If you like, you can use the formula for the sum of the series and solve for n.

  Sn = a1(r^n -1)/(r -1)

Substituting a1=5, r=2, we get ...

  315 = 5(2^n -1)/(1) . . . . . formula with numbers filled in

  63 = 2^n -1 . . . . . . . . . . divide by 5

  64 = 2^n = 2^6 . . . . . . . add 1, write 64 as a power of 2

  n = 6 . . . . . . . . . . . . . . . . match exponents (equivalently, take the log to the base 2)

There are 6 terms in the series.

-22

times both sides by 2, times () by 8, add alile terms, move terms, add alike and caculate divide both sides by 3

the answer is two. hope this !