JEE PYQ: Sequence And Series Question 69
Question 69 - 2019 (12 Jan Shift 2)
The product of three consecutive terms of a G.P. is 512. If 4 is added to each of the first and the second of these terms, the three terms now form an A.P. Then the sum of the original three terms of the given G.P. is:
(1) 36
(2) 32
(3) 24
(4) 28
Show Answer
Answer: (4)
Solution
Let three terms of a G.P. be $\frac{a}{r}$, $a$, $ar$
$\frac{a}{r} \cdot a \cdot ar = 512$
$a^3 = 512$
$a = 8$
4 is added to each of the first and the second of three terms then three terms are $\frac{8}{r} + 4, 8 + 4, 8r$
$\therefore \frac{8}{r} + 4, 12, 8r$ form an A.P.
$\therefore 2 \times 12 = \frac{8}{r} + 8r + 4$
$\Rightarrow 2r^2 - 5r + 2 = 0$
$\Rightarrow (2r - 1)(r - 2) = 0$
$\Rightarrow r = \frac{1}{2}$ or $2$
Therefore, sum of three terms $\frac{8}{2} + 8 + 16 = 28$
BETA
