If $p^{t h}, 2 p^{t h}, 4 p^{t h}$ terms of an A.P. are in G.P. then common ratio of G.P. is

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Solution

The correct option is C 2
$t_{p} = a + (p - 1) d$
$t_{2 p} = a + (2 p - 1) d$
$t_{4 p} = a + (4 p - 1) d$
$r = \frac{t_{2 p}}{t_{p}} = \frac{t_{4 p}}{t_{2 p}}$
$\Rightarrow r = \frac{t_{2 p} - t_{4 p}}{t_{p} - t_{2 p}}$
$= \frac{- 2 p}{- p}$
$= 2$

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