Question

The 10th common term between the series 3 + 7 + 11 + ... and 1 + 6 + 11 + .... is

• A. 191
• B. 193
• C. 211
• D. None of these

Answer 1

The correct option is A 191

$n_1^{th}$ term of series 1 is $=3+4(n_1-1)$

And $n_2^{th}$ term of series 2 is $=1+5(n_2-1)$

If $n_1^{th}$ and $n_2^{th}$ terms of series 1 and series 2 respectively are equal

$\Rightarrow n_2=\frac{3+4n_1}{5}$

Values of $n_1$ when $n_2$ is integer are $=3,8,13,18,23,28,33,38,43,48\dots$

For the ${10}^{th}$ Common Term $n_1=48$

Common Term $=3+(48-1)4=191$