Question

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

• A. $24$
• B. $26$
• C. $25$
• D. $20$

Answer 1

Answer: (D)

$20$

As both series are in AP.

In first series, first term is $2$ and common difference $3$.

In second series, first term is $3$ and common difference $2$.

Let $n^{th}$ term of first AP is equal to the $m^{th}$ term of second AP then

$a_n=a_m$

$2+(n-1)\times 3=3+(m-1)\times 2$

$2+3n-3=3+2m-2$

$3n=2(m+1)$

Let $\frac{n}{2}=\frac{m+1}{3}=k$

$n=2k\le 50$ and $m=3k-1\le 60$

$n\le 25$ and $k\le \frac{61}{3}\le 20$ as $k$ can not be fraction.

Hence, there are $20$ terms common in both series.