Question

The number of terms common between the two series $2+5+8+...$ up to $50$ terms and $3+5+7+9+...$ up to $60$ terms are

• A. $24$
• B. $26$
• C. $25$
• D. None of these

Answer 1

Answer: (D)

Let $m^{th}$ term of first $A.P$. be equal to the $n^{th}$ term of the second $A.P$. then $2,5,8,....50$ terms, series $1$
$3,5,7,...,60$ terms, series $2$
common series $5,11,17,...,119$
$40^{th}$ term of series $1=59^{th}$ term of series $2=119$ = last term of common series
$\Rightarrow a_n=5+\left(n-1\right)d\Rightarrow 119+1=6n\Rightarrow n=20$.
$\therefore$ Number of common terms are $20$.