Question

Solve the following series. Remember to use your formulas and indicate your final answer. Find the sum of the first 13 terms of: 1, 2, 4, 8, 16, ...

Answer 1

Answer

Sum of the first 13 terms = 8191

Explanation

The sum of terms in a geometric term is given as

$S_n=\frac{a\lbrack r^n-1\rbrack}{r-1}$

where

a = first term = 1

r = common ratio = ratio of consecutive terms = (Second term)/(First term) = (2/1) = 2

n = number of terms = 13

$\begin{gathered} S_n=\frac{a\lbrack r^n-1\rbrack}{r-1} \\ S_{13}=\frac{1\lbrack2^{13}-1\rbrack}{2-1}=\frac{8192-1}{1}=8191 \end{gathered}$

Hope this Helps!!!