jee-main 2022 Q64

jee-main · India · session1_25jun_shift2 Geometric Sequences and Series Finite Geometric Sum and Term Relationships
The sum $1 + 2 \cdot 3 + 3 \cdot 3^2 + \ldots + 10 \cdot 3^9$ is equal to
(1) $\frac{2 \cdot 3^{12} + 10}{4}$
(2) $\frac{19 \cdot 3^{10} + 1}{4}$
(3) $5 \cdot 3^{10} - 2$
(4) $\frac{9 \cdot 3^{10} + 1}{2}$ 
The sum $1 + 2 \cdot 3 + 3 \cdot 3^2 + \ldots + 10 \cdot 3^9$ is equal to\\
(1) $\frac{2 \cdot 3^{12} + 10}{4}$\\
(2) $\frac{19 \cdot 3^{10} + 1}{4}$\\
(3) $5 \cdot 3^{10} - 2$\\
(4) $\frac{9 \cdot 3^{10} + 1}{2}$
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