Question

Number of identical terms in the sequence $2,5,8,11,$ upto 100 terms and $3,5,7,9,11,\dots$ upto 100 terms are

• A. 17
• B. 33
• C. 50
• D. 147

Answer 1

The correct option is B 33

$2,5,8,11\text{... upto 100 terms}$

$\text{This is a}AP\text{with}a=2\text{d=}3$

$a_{100}=2+99\left(3\right)=299$

$3,5,7,9\text{... upto 100 terms}$

$\text{This is a}AP\text{with}a=3\text{d=}2$

$a_{100}=3+99\left(2\right)=201$

Common terms in both sequences are:

$5,11,17,...197$

$a_n=a+(n-1)d$

$197=5+(n-1)6$

$n=33$