Answer:
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.
