In an increasing geometric progression of positive terms, the sum of the second and sixth terms is 703 and the product of the third and fifth terms is 49 . Then the sum of the 4^th~,6^th~ and 8^th~ terms is equal to

aligned& T_2+T_6=703 \\& ar+ar^5=703 \\& ~T_3 ~T_5=49 \\& ar^2 ar^4=49 \\& a^2 r^6=49 \\& ar^3=+7, a=7r^3 \\& ar(1+r^4)=703 \\& 7r^2(1+r^4)=703, r^2=t \\& 1t(1+t^2)=103 \\& 3 t^2-10 t+3=0 \\& t=3, 13 \\& Increasing G.P. r^2=3, r=3 \\& ~T_4+T_6+T_8 \\& =ar^3+ar^5+ar^7 \\& =ar^3(1+r^2+r^4) \\& =7(1+3+9)=91aligned

In an increasing geometric progression of positive terms, the sum of the second and sixth terms is \frac{70}{3} and the product of the third and fifth terms is 49 . Then the sum of the 4^{{th}{~}},6^{{th}{~}} and 8^{{th}{~}} terms is equal to: Sequence & Series (Mathematics)

\begin{aligned}\n& \mathrm{T}_2+\mathrm{T}_6=\frac{70}{3} \\\n& \mathrm{ar}+\mathrm{ar}^5=\frac{70}{3} \\\n& \mathrm{~T}_3 \cdot \mathrm{~T}_5=49 \\\n& \mathrm{ar}^2 \cdot \mathrm{ar}^4=49 \\\n& \mathrm{a}^2 \mathrm{r}^6=49 \\\n& \mathrm{ar}^3=+7, \mathrm{a}=\frac{7}{\mathrm{r}^3} \\\n& \mathrm{ar}\left(1+\mathrm{r}^4\right)=\frac{70}{3} \\\n& \frac{7}{\mathrm{r}^2}\left(1+\mathrm{r}^4\right)=\frac{70}{3}, \mathrm{r}^2=\mathrm{t} \\\n& \frac{1}{\mathrm{t}}\left(1+\mathrm{t}^2\right)=\frac{10}{3} \\\n& 3 \mathrm{t}^2-10 \mathrm{t}+3=0 \\\n& \mathrm{t}=3, \frac{1}{3} \\\n& \text { Increasing G.P. } \mathrm{r}^2=3, \mathrm{r}=\sqrt{3} \\\n& \mathrm{~T}_4+\mathrm{T}_6+\mathrm{T}_8 \\\n& =\mathrm{ar}^3+\mathrm{ar}^5+\mathrm{ar}^7 \\\n& =\mathrm{ar}^3\left(1+\mathrm{r}^2+\mathrm{r}^4\right) \\\n& =7(1+3+9)=91\n\n\end{aligned}\n

Explanation

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