Question

Find the sum of the first 10 terms of the following sequence. Round to the nearesthundredth if necessary.15, 5,53'Sum of a finite geometric series:ai – ajrSn1 - rAnswer:Submit Answerattempt 1 out of 2

Answer 1

Given Data,

$\begin{gathered} a_1=15 \\ r=\frac{1}{3} \end{gathered}$

The sum of first 10 terms can be determined as,

$\begin{gathered} S_{10}=\frac{a_1(1-r^{10})}{1-r} \\ =\frac{15(1-(\frac{1}{3})^{10})}{1-\frac{1}{3}} \\ =\frac{15(3^{10}-1)\times3}{2\times3^{10}} \\ =22.4996 \\ \approx22.50 \end{gathered}$

Thus, the required sum is 22.50.