olivite wrote:
Fluke what does GP stand for? And what is the name of the formula you are referencing?
GP is Geometric Progression, where the ratio between two consecutive terms is always same.
According to the question, this series is a Geometric Series.
As,
\(A_2=A_1*k \hspace{3} OR \hspace{3} \frac{A_2}{A_1}=k\)
\(A_3=A_2*k \hspace{3} OR \hspace{3} \frac{A_3}{A_2}=k\)
\(A_4=A_3*k \hspace{3} OR \hspace{3} \frac{A_4}{A_3}=k\)
\(A_5=A_4*k \hspace{3} OR \hspace{3} \frac{A_5}{A_4}=k\)
For such series, the \(n^{th}\) term can be found using following formula:
\(A_n=A_1*k^{(n-1)}\)
Where,
\(k=\)
ratio between two consecutive terms\(A_1=\)
first term of the series\(n=\)
index of the term we are trying to find.Thus,\(25^{th}\)
term of the series, \(A_{25}=A_1*k^{(25-1)}\)
\(9^{th}\)
term of the series, \(A_{9}=A_1*k^{(9-1)}\)
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