JEE Main 2022 · MathsNumerical answerNumerical valueMediumMulti-step

JEE Main 25 June 2022, Shift 1, Maths Q30

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

The greatest integer less than or equal to the sum of first 100 terms of the sequence

\frac{1}{3},\frac{5}{9},\frac{19}{27},\frac{65}{81},\ldots

is equal to __________.

Official answer

NTA final key.

Chapter: Sequences and Series
Topic: AP and GP
Idea tested: GP Sum of n terms

Same idea in other shifts

Asked 10× in all

6 Apr 2026, Shift 1 · Q24For the functions $f(\theta)=\alpha\tan^2\theta+\beta\cot^2\theta$ , and $g(\theta)=\alpha\sin^2\theta+\beta\cos^2\theta$ ,…HardNumerical value
3 Apr 2025, Shift 1 · Q22All five letter words are made using all the letters A, B, C, D, E and arranged as in an English dictionary with serial numbers. Let the…HardNumerical value
29 Jan 2024, Shift 1 · Q7If in a G.P. of 64 terms, the sum of all the terms is 7 times the sum of the odd terms of the G.P, then the common ratio of the G.P. is…MediumSingle correct
28 Jul 2022, Shift 2 · Q86If $\frac{6}{3^{12}}+\frac{10}{3^{11}}+\frac{20}{3^{10}}+\frac{40}{3^9}+...+\frac{10240}{3}=2^n\cdot m$ , where m is odd, then $m\cdot n$ …MediumNumerical value
25 Jun 2022, Shift 1 · Q4Let $f:\mathbf{N}\to\mathbf{R}$ be a function such that $f(x+y)=2f(x)\,f(y)$ for natural numbers $x$ and $y$ . If $f(1)=2$ , then the value…MediumSingle correct
25 Jun 2022, Shift 1 · Q8If $\frac{1}{2\cdot3^{10}}+\frac{1}{2^2\cdot3^9}+\ldots+\frac{1}{2^{10}\cdot3}=\frac{K}{2^{10}\cdot3^{10}}$ , then the remainder when K is…MediumSingle correct
9 Jan 2020, Shift 2 · Q57Let $a_n$ be the $n^{\mathrm{th}}$ term of a G.P. of positive terms. If $\sum_{n=1}^{100}a_{2n+1}=200$ and $\sum_{n=1}^{100}a_{2n}=100$ ,…MediumSingle correct
5 Sep 2020, Shift 1 · Q57If $2^{10}+2^{9}\cdot3^{1}+2^{8}\cdot3^{2}+....+2\cdot3^{9}+3^{10}=S-2^{11}$ , then S is equal to :MediumSingle correct

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.