JEE Main 2024 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 6 April 2024, Shift 1, Maths Q24

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

Let the first term of a series be

T_1=6

and its

r^{\text{th}}

term

T_r=3T_{r-1}+6^r

r=2,3,\ldots\ldots, n

. If the sum of the first

n

terms of this series is

\frac{1}{5}\left(n^2-12n+39\right)\left(4\cdot6^n-5\cdot3^n+1\right)

, then

n

is equal to __________.

Official answer

NTA final key.

Chapter: Sequences and Series
Topic: Arithmetico-Geometric Series
Idea tested: AGP Recurrence Relation

Same idea in other shifts

Asked 3× in all

29 Jul 2022, Shift 2 · Q6Let $\{a_n\}_{n=0}^{\infty}$ be a sequence such that $a_0=a_1=0$ and $a_{n+2}=3a_{n+1}-2a_n+1,\ \forall n\geq 0$ . Then…HardSingle correct
29 Jun 2022, Shift 1 · Q12Let $\{a_n\}_{n=0}^{\infty}$ be a sequence such that $a_0 = a_1 = 0$ and $a_{n+2} = 2a_{n+1} - a_n + 1$ for all $n \ge 0$ . Then,…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.