Question

The number of terms which are identical in the sequence $2,5,8,11,\dots \text{upto}60\text{terms}$ and $3,5,7,9,\dots \text{upto}50\text{terms}$, is

• A. $16$
• B. $19$
• C. $18$
• D. $17$

Answer 1

The correct option is D $17$

$2,5,8,11,\dots \text{upto}60\text{terms}$
$T_{60}=2+(60-1)3=179$

$3,5,7,9,\dots \text{upto}50\text{terms}$
$T_{50}=3+(50-1)2=101$

Now, the common difference of first A.P. is $3$
and the common difference of second A.P. is $2$.
Therefore, the common difference of the A.P. formed by the common terms of both the A.P. $=\text{L.C.M.}(3,2)=6$
The first common term is $5$.

Let there be $n$ common terms.
The last term of the A.P. formed by the common terms of both the A.P. should be less than or equal to $101.$
i.e., $5+(n-1)6\le 101$
$\Rightarrow n\le 17$

Hence, the number of common terms in both the A.P. is $17$.