Question

Find the number of common terms in the following sequences (each of which is an A.P) which are less than $10,000$.
$S_1:37,103,169,\cdots$
$S_2:17,82,147,\cdots$

• A. $5$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is B $2$

$37+66a=17+65b$
$20+66a=65b$
$b=\frac{20+66a}{65}=\frac{65a}{65}+\frac{a+20}{65}$
For $a=45$, we will get the first term common
$37+66\times 45=3007$
LCM of $65,66$ is $4290$
So the next term is $7297$
Hence number of common terms will be $2$