JEE Main 2024 — 27 January, Shift 1 — Question 6

$4,9,14,19, \ldots$, up to $25^{\text {th }}$ term

$\mathrm{T}_{25}=4+(25-1) 5=4+120=124$

$3,6,9,12, \ldots$, up to $37^{\text {th }}$ term

$\mathrm{T}_{37}=3+(37-1) 3=3+108=111$

Common difference of $I^{\text {st }}$ series $\mathrm{d}_{1}=5$

Common difference of $\mathrm{II}^{\text {nd }}$ series $\mathrm{d}_{2}=3$

First common term $=9$, and their common difference $=15\left(\mathrm{LCM}\right.$ of $\mathrm{d}_{1}$ and $\left.\mathrm{d}_{2}\right)$

then common terms are $9,24,39,54,69,84,99$