Question

find the Sn for the GP: 2, -2, 2, -2.​

Answer 1

SOLUTION

TO DETERMINE

$\sf{The \: S_n \: for \: the \: GP \: \: \: 2,-2,2,-2,.....}$

FORMULA TO BE IMPLEMENTED

If in a Geometric Progression

First term = a and common ratio = r then

The Sum of the first n terms

$\displaystyle \sf {S_n = a \times \frac{ {r}^{n} - 1 }{r - 1} } \: \: \: when \: \: r > 1$

$\displaystyle \sf {S_n = a \times \frac{ 1 - {r}^{n} }{1 - r} } \: \: \: when \: \: r < 1$

EVALUATION

Here the given Geometric Progression is

2 , - 2 , 2 , - 2 , ........

First term = a = 2

Common Ratio = r = - 1 ( < 1 )

Hence the required sum of first n terms

$\displaystyle \sf {S_n = 2 \times \frac{ 1 - {( - 1)}^{n} }{1 - ( - 1)} }$

$\implies \displaystyle \sf {S_n = 2 \times \frac{ 1 - {( - 1)}^{n} }{2} }$

$\implies \displaystyle \sf {S_n = 1 - {( - 1)}^{n} }$

FINAL ANSWER

$\boxed{\displaystyle \sf { \: \: S_n = 1 - {( - 1)}^{n} \: }}$

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The G.M. of 3 and 24 with weight 2 and 1 respectively is

(A) 8(B) 4(C) 6(D) 9

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