Determine Sn for the geometric series? f(1)=2, r=-2, n=12

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Determine Sn for the geometric series? f(1)=2, r=-2, n=12

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Answer 1 · 2018-06-21T13:52:14

$S_{12} = \frac{8190}{11}$ $S_(12)=8190/11$

Explanation:

$the sum to n terms of a geometric sequence is$ $"the sum to n terms of a geometric sequence is"$

$∙ x S_{n} = \frac{a (r^{n} - 1)}{r - 1}$ $•color(white)(x)S_n=(a(r^n-1))/(r-1)$

$where a is the first term and r the common ratio$ $"where a is the first term and r the common ratio"$

$here a = 2, r = - 2 and n = 12$ $"here "a=2,r=-2" and "n=12$

$S_{12} = \frac{2 ({(- 2)}^{12} - 1)}{12 - 1}$ $S_(12)=(2((-2)^(12)-1))/(12-1)$

$\times \times \times = \frac{2 (4096 - 1)}{11} = \frac{8190}{11}$ $color(white)(xxxxxx)=(2(4096-1))/11=8190/11$

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Determine Sn for the geometric series? f(1)=2, r=-2, n=12

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