JEE Main 2022 · MathsMultiple choiceSingle correctEasyCalculation

JEE Main 25 June 2022, Shift 2, Maths Q8

Question 8 of 90 in this shift, Maths question 8 of 30, Section A.

The sum

1 + 2 \cdot 3 + 3 \cdot 3^2 + ....... + 10 \cdot 3^9

is equal to :

(1) $\frac{2 \cdot 3^{12} + 10}{4}$
(2) $\frac{19 \cdot 3^{10} + 1}{4}$ Official answer
(3) $5 \cdot 3^{10} - 2$
(4) $\frac{9 \cdot 3^{10} + 1}{2}$

Official answer

Option 2

NTA final key.

Chapter: Sequences and Series
Topic: Arithmetico-Geometric Series
Idea tested: Sum of Finite AGP

Same idea in other shifts

Asked 3× in all

6 Apr 2023, Shift 2 · Q23If $(20)^{19}+2(21)(20)^{18}+3(21)^2(20)^{17}+\ldots+20(21)^{19}=k(20)^{19}$ , then $k$ is equal to ___________.HardNumerical value
11 Apr 2023, Shift 1 · Q25Let $S = 109 + \frac{108}{5} + \frac{107}{5^2} + \ldots + \frac{2}{5^{107}} + \frac{1}{5^{108}}$ . Then the value of $(16S - (25)^{-54})$ …MediumNumerical value

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.