JEE Main 2022 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 29 July 2022, Shift 2, Maths Q6

Question 6 of 90 in this shift, Maths question 6 of 30, Section A.

Let

\{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

a_{25}a_{23}-2a_{25}a_{22}-2a_{23}a_{24}+4a_{22}a_{24}

is equal to

(1) $483$
(2) $528$ Official answer
(3) $575$
(4) $624$

Official answer

Option 2

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

6 Apr 2024, Shift 1 · Q24Let 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…HardNumerical value
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.