Let a,b,c be the 7th, 11th and 13th terms respectively of a non-constant A.P.

Question

Let $a,b,c$ be the 7th, 11th and 13th terms respectively of a non-constant A.P. If these are also three consecutive terms of a G.P., then $\dfrac ac$ is equal to:

Accepted Answer

$a=A+6D$, $b=A+10D$, $c=A+12D$. Since $b^2=ac$: $(A+10D)^2=(A+6D)(A+12D) \Rightarrow 14D+A=0 \Rightarrow A=-14D.$

$$a=-8D,\ c=-2D \implies \frac ac = \frac{-8D}{-2D}=4.$$

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