The product of three consecutive terms of a G.P. is 512 .
Question:

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 from an A.P. Then the sum of the original three terms of the given G.P. is

  1. 36

  2. 24

  3. 32

  4. 28


Correct Option: , 4

Solution:

Let terms are $\frac{\mathrm{a}}{\mathrm{r}}, \mathrm{a}, \mathrm{ar} \rightarrow$ G.P

$\therefore a^{3}=512 \Rightarrow a=8$

$\frac{8}{r}+4,12,8 r \rightarrow$ A.P.

$24=\frac{8}{r}+4+8 r$

$\mathrm{r}=2, \mathrm{r}=\frac{1}{2}$

$r=2(4,8,16)$

$r=\frac{1}{2}(16,8,4)$

$\operatorname{Sum}=28$

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