Mathematics · Sequence and Series

JEE Main 2024 — 1 February, Shift 1 — Question 24

Let $3,7,11,15, \ldots, 403$ and $2,5,8,11, \ldots, 404$ be two arithmetic progressions. Then the sum, of the common terms in them, is equal to $\qquad$ .

Answer: 6699

Numerical answer — enter this value.

Step-by-step solution

$3,7,11,15, \ldots ., 403$

$2,5,8,11, \ldots, 404$

$\operatorname{LCM}(4,3)=12$ $11,23,35, \ldots$ .

let $(403)$

$403=11+(n-1) \times 12$

$\frac{392}{12}=n-1$

$33 \cdot 66=n$

$n=33$

$\operatorname{Sum} =\frac{33}{2}(22+32 \times 12)$

$=6699$

Answer key and solution verified before publishing.

Practise Sequence and Series

Start with this question, then two more from the same chapter — with a tutor that explains every step. Free.

Solve a similar one free

Exam: JEE Main 2024
Paper: 1 February, Shift 1
Subject: Mathematics
Chapter: Sequence and Series
Topic: Arithmetic Progression

Let 3, a, b, c be in A.P. and 3, a-1, b+1, c+9 be in G.P. Then, the arithmetic mean of a, b and c is :

Answer: 6699

Step-by-step solution

Practise Sequence and Series

More Sequence and Series questions from this paper