Question

The value of the largest term common to the sequences $1,11,21,31,..$ upto $100$ terms and $31,36,41,46,...$ upto $100$ terms, is

• A. $281$
• B. $381$
• C. $471$
• D. $521$

Answer 1

The correct option is D $521$

Sequence $1,11,21,31,..$ has common difference$=10$ and
sequence $31,36,41,46,..$ has common difference$=5$.
Hence, the sequence with common terms has common difference LCM$(10,5)=10$
The first common term is $31$
Hence, the sequence is $31,41,51,61,..$
Now, $T_{100}$ of first sequence$=1+(100-1)10=991$ .....$\left(1\right)$
and $T_{100}$ of second sequence$=31+(100-1)5=526$
Value of the largest common term$<526$
$\therefore T_n$ of eqn$\left(1\right)$ is $31+(n-1)10=10n+21$
Hence $T_{50}=10\times 50+21=500+21=521$ is the largest common term.