Let a_1, a_2, a_3, ... . be a G.P. of increasing positive terms such that a_2 * a_3 * a_4=64 and a_1+a_3+a_5=(813 / 7). Then a_3+ a_5+ a_7 is equal to :

ar . ar^2 . ar^3=64 a^3 r^6=64 => ar^2=4 a+ ar^2+ ar^4=(813 / 7) r^2=28 a r^2+a r^4+a r^6= ? \ ar^2(1+ r^2+ r^4)=4(1+28+784)=3252

Let a 1 a 2 a 3 be a G P of increasing positive terms ... | null (Mathematics)

JEE Mains 2026 21st January Shift 1

Mathematics

Let

\mathrm{a}_{1}, \mathrm{a}_{2}, \mathrm{a}_{3}, \ldots

. be a G.P. of increasing positive terms such that

a_{2} \cdot a_{3} \cdot a_{4}=64

and

a_{1}+a_{3}+a_{5}=\frac{813}{7}

. Then

\mathrm{a}_{3}+\mathrm{a}_{5}+\mathrm{a}_{7}

is equal to :

3256

3252

3244

3248

. \mathrm{ar}^{2} . \mathrm{ar}^{3}=64\\

\mathrm{a}^{3} \mathrm{r}^{6}=64 \quad \Rightarrow \mathrm{ar}^{2}=4\\

\mathrm{a}+\mathrm{ar}^{2}+\mathrm{ar}^{4}=\frac{813}{7}\\

\mathrm{r}^{2}=28\\

a r^{2}+a r^{4}+a r^{6}=

\\ \operatorname{ar}^{2}\left(1+\mathrm{r}^{2}+\mathrm{r}^{4}\right)=4(1+28+784)=3252

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