Question

Find the sum of the first 10 terms of the geometric sequence: an= 27(.1)^n-1

Answer 1

We have a geometric sequence:

$a_n=27\cdot(0.1)^{n-1}$

The sum of a certain amount of terms of a geometric sequence is given by:

Where a=27, r=0.1 and n is the number of terms you want to add. So the sum of the first ten terms is given by:

$S_{10}=\frac{27\cdot((0.1)^{10}-1)}{0.1-1}=30$