Question

What is the S5 for 1000+ 500+250+...

Answer 1

I'm guessing we have

S1 = 1000

S2 = 1000 + 500

S3 = 1000 + 500 + 250

S4 = 1000 + 500 + 250 + 125

S5 = 1000 + 500 + 250 + 125 + 62.5

Just adding that up, S5 is

Answer: 1937.5

Do they want you to use the geometric series formula?  We'll check it that way.

We have first term a=1000 and common ratio r=1/2.  In general

$S_n = \dfrac{a(1 - r^n)}{1-r}$

For us that's

S5 = (1000 (1 - (1/2)^5))/(1 - 1/2) = 2000(1 - 1/32)

                        = 2000(31)/32 = 62000/32 = 1937.5     √

Math works!