Let $\mathrm{a}, \mathrm{b}$ and c be the $7^{\text {th }}, 11^{\text {th }}$ and $13^{\text {th }}$ terms respectively of a non-constant A.P. If these are also the three consecutive terms of a G.P., then $\frac{a}{c}$ is equal to
Select the correct option:
A
$\frac{1}{2}$
B
4
C
$\frac{7}{13}$
D
7
✓ Correct! Well done.
✗ Incorrect. Try again or view the solution.
Solution
Let first term and common difference be A and D respectively.
$$
\begin{array}{ll}
\therefore & a=A+6 D, b=A+10 D \\
& \text { and } c=A+12 D \\
\because & a, b, c \text { are in } G \cdot P . \\
\therefore & b^2=a \cdot c . \\
\therefore & (A+10 D) 2=(A+6 D)(A+12 D) \\
\therefore & 14 D+A=0 \\
\therefore & A=-14 D \\
\therefore & a=-8 D, b=-4 D \text { and } c=-2 D \\
\therefore & \frac{a}{c}=\frac{-8 D}{-2 D}=4
\end{array}
$$
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