JEE MainMathematicsModerateSequences and Series

A geometric progression (G.P.) consists of even number of terms.
If the sum of all terms is times the sum of terms occupying odd
places. Then common ratio is

Show answer and solution

a + ar + ar^{2} + \_\_\_\ ar^{2n - 1} = 5\lbrack a + ar^{2} + ar^{4} + \_\_\_\_ ar^{2n - 2})

\frac{r^{2n} - 1}{r - 1} = \frac{5(r^{2n} - 1)}{(r - 1)(r + 1)} \Rightarrow r = 4

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

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