Question

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

• A. 381
• B. 471
• C. 281
• D. 521

Answer 1

The correct option is D

521

${100}^{th}$ term of $1,11,21,31,....is1+(100-1)10=991.{100}^{th}$ term of $31,36,41,46,....is31+(100-1)5=526.$ Let the largest common term be $526.$ Then.
526=31+(n-1)10
$\Rightarrow n=50.5$

But n is an interger; hence n=50. Hence, the largest common term is $31+(50-1)10=521.$