In a geometric progression the ratio of the sum of the first 5 terms to the sum of their reciprocals is 49 and sum of the first and the third term is 35.The fifth term of the G.P. is

# In a geometric progression the ratio of the sum of the first 5 terms to the sum of their reciprocals is 49 and sum of the first and the third term is 35.The fifth term of the G.P. is

1. A

7

2. B

7/2

3. C

7/4

4. D

7/8

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### Solution:

Let five terms in G.P. be

Then $\frac{a\left({r}^{-2}+{r}^{-1}+1+r+{r}^{2}\right)}{\left(1/a\right)\left({r}^{2}+r+1+{r}^{-1}+{r}^{-2}\right)}=49$

Also, $\frac{a}{{r}^{2}}+a=35$

Therefore  is not possible

Thus, $a=7$ and $a/{r}^{2}=28.$

Now, fifth term $=a{r}^{2}=a\left(\frac{a}{28}\right)=\frac{7}{4}$

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