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. none of these.

Answer 1

Answer: (D)

Let mth term of the first sequence be equal to the n^th term of the second sequence. Then
$1+(m-1)10=31+(n-1)5$
$\Rightarrow 10m-9=5n+26$
$\Rightarrow 10m-35=5n$
$\Rightarrow 2m-7=n\le 100$
$\Rightarrow 2m\le 107$
$\Rightarrow m\le 53\frac{1}{2}$
$\therefore$ largest value of $m=53$
largest term $=1+52\times 10=521$