JEE Main 2023 (Online) 30th January Evening ShiftQuestion 1
The $8^{th}$ common term of the series
$S_1=3+7+11+15+19+\ldots$
$S_2=1+6+11+16+21+\ldots$ is
Sequence and Series · Arithmetic Progression
Answer$151$
Solution
Formulas used. (1) Common terms of two A.P.s form an A.P. with difference $\operatorname{lcm}(d_1,d_2)$(2) $T_n=a+(n-1)d$Step 1 - First common term. $S_1$: $3,7,11,\dots$ ($d=4$); $S_2$: $1,6,11,\dots$ ($d=5$). The first common term is $11$. Step 2 - The common A.P. Difference $\operatorname{lcm}(4,5)=20$: $11,31,51,\dots$ Step 3 - Eighth term. $$11+7\times20=151 .$$ Answer: 151