Mathematics · Sequence and Series

JEE Main 2026 — 28 January, Evening Shift — Question 20

$\frac{6}{3^{26}}+\frac{10.1}{3^{25}}+\frac{10.2}{3^{24}}+\frac{10.2^{2}}{3^{23}}+\ldots+\frac{10.2^{24}}{3}$ is equal to

Answer: B

$\quad S=\frac{6}{3^{26}}+\frac{10}{3^{25}}\left[\frac{(6)^{25}-1}{6-1}\right]$

$\mathrm{S}=\frac{6}{3^{26}}+\frac{10}{3^{25}}\left[\frac{6^{25}-1}{5}\right]$

$\mathrm{S}=\frac{2}{3^{25}}+2\left[2^{25}-\frac{1}{3^{25}}\right]$

$\mathrm{S}=2^{26}$

Answer key and solution verified before publishing.

Start with this question, then two more from the same chapter — with a tutor that explains every step. Free.