SOLUTION: If the first term of a geometric sequence is 0.9 and it's ratio is 0.8, what is the sum of the first five terms?

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Question 1161642: If the first term of a geometric sequence is 0.9 and it's ratio is 0.8, what is the sum of the first five terms?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

In General we write a Geometric Sequence like this:
{ a, ar,+ar%5E2, ar%5E3, ... }
where:
a is the first term, and
r is the factor between the terms (called the "common ratio")
If the first term of a geometric sequence is 0.9 and it's ratio is+0.8, we have
a=0.9
r=0.8
and first five terms are:
a=0.9
ar=0.9%2A0.8=0.72
ar%5E2=0.9%2A0.8%5E2=0.576
ar%5E3=0.9%2A0.8%5E3=0.4608
ar%5E4=0.9%2A0.8%5E4=0.36864
their sum is:
sum=0.9%2B0.72%2B0.576%2B0.4608%2B0.36864=3.02544
or, use sum formula
sum=a%28%281-r%5En%29%2F%281-r%29%29......substitute given
sum=0.9%28%281-0.8%5En%29%2F%281-0.8%29%29
fifth term->n=5
the sum of the first five terms, will be
sum=0.9%28%281-0.8%5E5%29%2F%281-0.8%29%29
sum=0.9%28%281-0.32768%29%2F0.2%29
sum=0.9%280.67232%2F0.2%29
sum=0.9%283.3616%29
sum=3.02544