How do you find the sum of the first 10 terms of the following geometric sequence 5, 10, 20, 40, 80, …….?

1 Answer
Alan P.
Feb 25, 2016

5115

Explanation:

a_0=5
r=2

We are asked for the sum of the first 10 terms i.e. a_0, a_1, ..., a_9
so n=9 in the general geometric sum formula:
color(white)("XXX")Sigma_(i=0)^n = a_0*(1-r^(n+1))/(1-r)

In this case we have
color(white)("XXX")Sigma_(i=0)^9 = 5*(1-2^10)/(1-2) = 5xx1023=5115

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