JEE Main 2023 · MathsNumerical answerNumerical valueMediumMulti-step

JEE Main 13 April 2023, Shift 1, Maths Q24

Question 24 of 90 in this shift, Maths question 24 of 30, Section B.

The sum to 20 terms of the series

2\cdot2^2-3^2+2\cdot4^2-5^2+2\cdot6^2-\ldots\ldots

is equal to ________.

Official answer

1310

NTA final key.

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

Same idea in other shifts

Asked 31× in all

2 Apr 2026, Shift 2 · Q5The sum $\frac{1^3}{1} + \frac{1^3 + 2^3}{1 + 3} + \frac{1^3 + 2^3 + 3^3}{1 + 3 + 5} + \ldots$ up to 8 terms, is:MediumSingle correct
4 Apr 2026, Shift 1 · Q7The first term of an A.P. of $30$ non-negative terms is $\frac{10}{3}$ . If the sum of this A.P. is the cube of its last term, then its…MediumSingle correct
6 Apr 2026, Shift 1 · Q6The sum of the first ten terms of an A.P. is 160 and the sum of the first two terms of a G.P. is 8. If the first term of the A.P. is equal…MediumSingle correct
8 Apr 2026, Shift 2 · Q5Let $\alpha = 3 + 4 + 8 + 9 + 13 + 14 + \ldots$ up to 40 terms. If $(\tan\beta)^{\frac{\alpha}{1020}}$ is a root of the equation…MediumSingle correct
2 Apr 2025, Shift 1 · Q19Let $a_1, a_2, a_3,\ldots$ be in an A.P. such that $\sum_{k=1}^{12}a_{2k-1}=-\frac{72}{5}a_1$ , $a_1\neq0$ . If $\sum_{k=1}^{n}a_k=0$ , then…MediumSingle correct
7 Apr 2025, Shift 2 · Q6Let $a_n$ be the $n^{\mathrm{th}}$ term of an A.P. If $S_n=a_1+a_2+a_3+\ldots+a_n=700$ , $a_6=7$ and $S_7=7$ , then $a_n$ is equal to :MediumSingle correct
5 Apr 2024, Shift 1 · Q25Let $a_1, a_2, a_3, \ldots$ be in an arithmetic progression of positive terms. Let…HardNumerical value
6 Apr 2024, Shift 2 · Q7A software company sets up $m$ number of computer systems to finish an assignment in 17 days. If 4 computer systems crashed on the start…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.