Mathematics, 16.07.2019 00:30 jaleewoodyard1
Find the sum of the geometric sequence. 1, 1/4, 1/16, 1/64, 1/256 a) 341 b) 1/192 c) 1/768 d) 341/256
Answers: 1
![1,\ \dfrac{1}{4};\ \dfrac{1}{16};\ \dfrac{1}{64};\ \dfrac{1}{256}\ \text{is geometric sequence}\\\\\text{the ratio is:}\ r=\dfrac{\frac{1}{4}}{1}=\dfrac{1}{4}\\\\\text{The sum of the numbers in a geometric sequence is:}\\\\S_n=\dfrac{a_1(1-r^n)}{1-r}\\\\a_1=1;\ r=\dfrac{1}{4}\\\\\text{substitute}\\\\S_5=\dfrac{1\cdot\left[1-\left(\dfrac{1}{4}\right)^5\right]}{1-\dfrac{1}{4}}=\dfrac{1-\dfrac{1}{1024}}{\dfrac{3}{4}}=\dfrac{1023}{1024}\cdot\dfrac{4}{3}=\dfrac{341}{256}\to D)](/tpl/images/0094/4185/f1f61.png)
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Find the sum of the geometric sequence. 1, 1/4, 1/16, 1/64, 1/256 a) 341 b) 1/192 c) 1/768 d) 341/25...
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