# Chapter 11 - Section 11.3 - Geometric Sequences and Series - Exercise Set - Page 854: 38

$s_{14}=\dfrac{5461}{24}=227.541$

#### Work Step by Step

Formula to calculate the sum of the first $n$ terms of a geometric sequence is: $s_n=\dfrac{a(1-r^n)}{(1-r)}$ Here, $r=\dfrac{a_2}{a_1}=-2$ As we are given that, $n=14$ Thus, $s_{14}=\dfrac{\dfrac{-1}{24}(1-(-2)^{14})}{(1+2)}$ or, $s_{14}=\dfrac{5461}{24}=227.541$

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