In a decreasing G.P. with common ratio such that , the ratio of fourth term to second term is & ratio of 3^rd term to the square of 2^nd term is 1/9 The sum up to infinite terms of this G.P. is find .

JEE MainMathematicsEasySequences and Series

In a decreasing G.P. with common ratio such that
$|x| < 1,x \neq 0$ , the ratio of fourth term to second term is $1/16$ &
ratio of 3^rd term to the square of 2^nd term is 1/9 The sum up to
infinite terms of this G.P. is $\lambda$ find $\ \frac{\lambda}{4}$ .

Show answer and solution

\frac{T_{4}}{T_{2}} = \frac{ax^{3}}{ax} = \frac{1}{16},x = \pm \frac{1}{4}

decreasing G.P. So

\ x = \frac{1}{4}

\frac{T_{3}}{T_{2}} = \frac{1}{9} \Rightarrow a = 9

\frac{a}{1 - x} = 12

Source: Grass-G / M-16 Mathematics Paper 25 Nov First.docx

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