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Profit Maximisation Condition for a Firm

Let a1, a2, a...

Question

Let $a_{1}$ , $a_{2}$ , $a_{3}$ , ... be in AP and $a_{p}$ , $a_{q}$ , $a_{r}$ be in GP. Then $a_{q}$ : $a_{p}$ is equal to

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Solution

The correct option is C

Let

$a_{p}$ = $a_{1}$ + (p - 1)d, $a_{q}$ = $a_{1}$ + (q - 1)d, $a_{r}$ = $a_{1}$ + (r - 1)d

as $a_{p}$ , $a_{q}$ , $a_{r}$ are in G.P.

$\frac{a_{q}}{a_{p}}$ = $\frac{a_{r}}{a_{q}}$ = $\frac{a_{q} - a_{r}}{a_{p} - a_{q}}$ (by law of proportions)

or $\frac{a_{q}}{a_{p}}$ = $\frac{a_{r}}{a_{q}}$ = $\frac{a_{1} + (q - 1) d - a_{1} - (r - 1) d}{a_{1} + (p - 1) d - a_{1} - (q - 1) d}$ = $\frac{q - r}{p - q}$ or $\frac{a_{q}}{a_{p}}$ = $\frac{q - r}{p - q}$ = $\frac{r - q}{q - p}$

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Similar questions

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Let a1, a2, a3, ... be in AP and ap, aq , ar be in GP. Then aq : ap is equal to

The correct option is C Let ap = a1 + (p - 1)d, aq = a1 + (q - 1)d, ar = a1 + (r - 1)d as ap, aq, ar are in G.P. aqap = araq = aq−arap−aq (by law of proportions) or aqap = araq = a1+(q−1)d−a1−(r−1)da1+(p−1)d−a1−(q−1)d = q−rp−q or aqap = q−rp−q = r−qq−p

Let $a_{1}$ , $a_{2}$ , $a_{3}$ , ... be in AP and $a_{p}$ , $a_{q}$ , $a_{r}$ be in GP. Then $a_{q}$ : $a_{p}$ is equal to