JEE PYQ: Sequence And Series Question 61
Question 61 - 2019 (09 Jan Shift 2)
Let a, b and c be the $7^{th}$, $11^{th}$ and $13^{th}$ 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:
(1) 2
(2) $\frac{1}{2}$
(3) $\frac{7}{13}$
(4) 4
Show Answer
Answer: (4)
Solution
Let first term and common difference be $A$ and $D$ respectively.
$\therefore a = A + 6D, b = A + 10D$
and $c = A + 12D$
Since, $a, b, c$ are in G.P.
Hence, relation between $a, b$ and $c$ is,
$\therefore b^2 = a.c$.
$\therefore (A + 10D)^2 = (A + 6D)(A + 12D)$
$\therefore 14D + A = 0$
$\therefore A = -14D$
$\therefore a = -8D, b = -4D$ and $c = -2D$
$\therefore \frac{a}{c} = \frac{-8D}{-2D} = 4$
BETA
