CAT 2023 Slot 3 QA Question 21: Let $a_n = 46 + 8n$ and $b_n = 98 + 4n$ be two sequences for natural numbers $n \leq 100$. Then, the sum of all terms common to both the sequences is

Question

Let $a_n = 46 + 8n$ and $b_n = 98 + 4n$ be two sequences for natural numbers $n \leq 100$. Then, the sum of all terms common to both the sequences is

Accepted Answer

The first sequence is

$54, 62, 70, \ldots, 846$

The second sequence is

$102, 106, 110, \ldots, 498$

A common term must be in the second sequence and also differ from 46 by a multiple of 8. The first such term is 102.

Common terms are therefore

$102, 110, 118, \ldots, 494$

This is an AP with f

Let an=46+8na_n = 46 + 8nan​=46+8n and bn=98+4nb_n = 98 + 4nbn​=98+4n be two sequences for natural numbers n≤100n \leq 100n≤100. Then, the sum of all terms common to both the sequences is