Question

$6,11,16,...$ is an arithmetic sequence. What is its next term? What is the least three digit number that comes as a term of this sequence?

Answer 1

Arithmetic sequence is $6,11,16,...$
Here $a_1=6,a_2=11,a_3=16$
Common difference $d=a_2-a_1=11-6=5$
Thus, next term $=a_4=a_3+d=16+5=21$
Now, $t_n\ge 100$
$a+(n-1)d\ge 100$
$6+(n-1)5\ge 100$
$(n-1)5\ge 94$
$n\ge 19.8=20$th term
Thus, $t_{20}=6+\left(19\right)\left(5\right)=6+95=101$