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If S, P and R are the sum, product and sum of the reciprocals of n terms of an increasing G.P. and Sn = Rn. Pk, then k is equal to

Option: 1

1


Option: 2

2


Option: 3

3


Option: 4

4


Answers (1)

best_answer

 

General term of a GP -

T_{n}= ar^{n-1}
 

- wherein

a\rightarrow first term

r\rightarrow common ratio

 

 

Sum of n terms of a GP -

S_{n}= \left\{\begin{matrix} a\frac{\left ( r^{n}-1 \right )}{r-1}, &if \: r\neq 1 \\ n\, a, & if \, r= 1 \end{matrix}\right.

 

- wherein

a\rightarrow first term

r\rightarrow common ratio

n\rightarrow number of terms    

 

 

S=\frac{a(1-r^{n})}{1-r},P=a^{a}r^{\frac{n(n-1)}{2}}

R=\frac{1}{a}+\frac{1}{ar}+\frac{1}{ar^{2}}................... to \; n\; terms = \frac{1-r^{n}}{a(1-r)r^{n-1}}

S^{n}=R^{n}P^{k}                  \Rightarrow \left ( \frac{S}{R} \right )^{n}=p^{k}\Rightarrow (a^{1}.r^{n-1})^{n}=P^{k}

\Rightarrow P^{2}=P^{k}                  \Rightarrow k=2                             

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