Question

What equation do I use to find the answer to the following problem?

Answer 1

What is the sum of the first five terms of the geometric sequence in which a1 = 10 and r = 1/2?

Answer 2

read it, at the middle of the page http://www.mathsisfun.com/algebra/sequences-sums-geometric.html
and then apply to your problem, then, post the answer, any of us can check.

Answer 3

I got S=55

Answer 4

I don't know how can you get it. I will solve it in 2 ways: counting my fingers and applying the formula from the page
1/ counting my fingers:
a1 = 10
a2 = 10*1/2 = 5
a3 = 5*1/2 = 5/2
a4= 5/2*1/2 = 5/4
a5= 5/4*1/2 = 5/8
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total a1+a2+a3+a4+a5= 10 +5+5/2+5/4+5/8 = \(\large \frac{80+40+20+10 +5}{8}=\frac{155}{8}\)
2/ apply formula
\[\sum_0^5 ar^k=a(\frac{1-r^5}{1-r})\] where a =10, r = 1/2
sum = 10* \(\large \frac{1- (1/2)^5}{1-1/2}\) = 10 * \(\large \frac{31}{16}= \frac{310}{16}=\frac{155}{16}\)
So, no matter what way you go, the answer must be the same. I prefer applying formula