What is the sum of the geometric sequence 1, 3, 9, … if there are 11 terms?

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What is the sum of the geometric sequence 1, 3, 9, … if there are 11 terms?

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Answer 1 · 2016-01-21T18:13:33

$S u m = 88573$ $Sum=88573$

Explanation:

$\frac{a_{2}}{a_{1}} = \frac{3}{1} = 3$ $a_2/a_1=3/1=3$

$\frac{a_{3}}{a_{2}} = \frac{9}{3} = 3$ $a_3/a_2=9/3=3$

$\Rightarrow$ $implies$ common ration $= r = 3$ $=r=3$ and $a_{1} = 1$ $a_1=1$

Number of terms $= n = 11$ $=n=11$

Sum of geometric series is given by

$S u m = \frac{a (1 - r^{n})}{1 - r} = \frac{1 (1 - 3^{11})}{1 - 3} = \frac{3^{11} - 1}{3 - 1} = \frac{177147 - 1}{2} = \frac{177146}{2} = 88573$ $Sum=(a(1-r^n))/(1-r)=(1(1-3^11))/(1-3)=(3^11-1)/(3-1)=(177147-1)/2=177146/2=88573$

$\Rightarrow S u m = 88573$ $implies Sum=88573$

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What is the sum of the geometric sequence 1, 3, 9, … if there are 11 terms?

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