If $a_{1}, a_{2}, a_{3}, . . . . . . . . . .$ are in AP then $a_{p}, a_{q}, a_{r}$ are in AP if $p, q, r$ are in:

A.P.

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G.P.

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H.P.

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None of these

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Solution

The correct option is A A.P.
If $a_{1}, a_{2}, a_{3}, . . . . . .$ are in AP
$∴ a_{2} - a_{1} = a_{3} - a_{2}$ (equation $01$ )
$a_{3} - a_{2} = a_{4} - a_{3}$ (equation $02$ )
.
.
.
$a_{p}, a_{q}$ and $a_{r}$ are in AP.
$a_{q} - a_{p} = a_{r} - a_{q}$ (equation $03$ )
Comparing equation $01, 02$ and $03$
$p, q, r$ are in AP

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