Question

The number of terms common between the two series $2+5+8+\cdots$ upto $50$ terms and the series $3+5+7+9+\cdots$ upto $60$ terms.

• A. $24$
• B. $26$
• C. $25$
• D. $Noneofthese$

Answer 1

The correct option is D $Noneofthese$

Series 1 : $2+5+8+..$
$T_m=2+(m-1)3=3m-1$
Series 2 : $3+5+7+...$
$t_n=3+(n-1)2=2n+1$
For common terms, $t_n=T_m$
$\Rightarrow 3m-1=2n+1$
$\Rightarrow 3m=2(n+1)$
For m to be a natural number, $n=2,5,8,..59$
Thus, number of common terms $=$ no. of terms of sequence $2,5,8,...,59$
$N^{th}$ term $=T_N=2+(N-1)3=3N-1$
$3N-1=59\Rightarrow N=20$