Question

The product of three consecutive terms of a G.P is 512 if 4 is added to each of first and second of these terms the three terms now form of an A.P then the sum of the original three terms of the given G.P

Answer 1

$\rule{300}{2}$

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Answer 2

Answer:

Sum of the original three terms of the given G.P is 28

Step-by-step explanation:

Given: Product of three consecutive terms of a G.P is 512

To find: the sum of the original three terms of the given G.P

Solution:

Let the three consecutive terms of a GP are:

$\frac{a}{r}, a , and a r$

Now, according to the question,

$\begin{aligned}&\Rightarrow \frac{a}{r} \cdot a \cdot a r=512 \\&\Rightarrow \mathrm{a}^{3}=512 \\&\therefore \mathrm{a}=8\end{aligned}$

Also, after adding 4 to first two terms,

$\begin{aligned}&\frac{8}{r}+4,8+4,8 r \text { are in } A P \\&\Rightarrow 2(12)=\frac{8}{r}+4+8 r \\&\Rightarrow 24=\frac{8}{r}+8 r+4 \Rightarrow 20=4\left(\frac{2}{r}+2 r\right) \\&\Rightarrow 5=\frac{2}{r}+2 r \\&\Rightarrow 2 r^{2}-5 r+2 a \\&\Rightarrow 2 r^{2}-4 r-r+2=0 \\&\Rightarrow 2 r(r-2)-1(r-2)=0 \\&\Rightarrow(r-2)(2 r-1)=0\end{aligned}$

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

∴$16,8,4(or) 4,8,16$ are the 3  terms of given G.P.

Sum of term is =28