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formula for finding the sum of the first n terms of a geometric sequences with a ratio between 0 and 1?
Is there a formula for finding the sum of the first n terms of a geometric sequences with a ratio between 0 and 1?
I have been searching all night tryin to find it with no luck. the usual axr^n-a/a-1 does not work for decimals. If there is no formula, can you explain why.
What I mean is the sum of the first n terms.
okay for example, ratio=.5, and a=1
1 2 3 4
1 1.5 1.75 1 .875
2 Answers
- Anonymous1 decade agoFavorite Answer
The formula is
Sn=a(1-r^n)/(1-r)
where a= the initial term
r= the common ratio.
when a=1, r=0.5
Sn=(1-0.5^n)/0.5=>
Sn=2-2^(1-n)
When n=4, then
S4=2-2^-3=>
S4=2-1/8=>
S4=15/8=>
S4=1.875
