Question

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

• A. $381$
• B. $471$
• C. $281$
• D. None of these

Answer 1

The correct option is D None of these

The general term of sequence $1,11,21,31,....100$ terms is $1+10n$ where $n$ goes from $0$ to $99$

The general term of sequence $31,36,\mathrm{41.....100}$ terms is $31+5k$ where $k$ goes from $0$ to $99$

For both sequences to have common term , $1+10n=31+5k$ for some values of $n,k$

$\Rightarrow 10n=30+5k$

$\Rightarrow 2n=6+k$

The largest even value of $k$ is $98$, so at $k=98$ , we get $n=52$

The largest common value is $1+10\times 52=521$

Therefore the correct option is $D$