Answer
$n=61$
Work Step by Step
We have to find the position of the term which is equal to $22$ in this arithmetic sequence:
$10, 10.2, 10.4, 10.6, . . .$
The common difference $d$ in our case is
$d=a_{n+1}-a_n=a_2-a_1=10.2-10=0.2.$.
We can find any term of the sequence using the formula
$a_n=a_1+d(n-1).$
In our conditions:
$a_1=10, d=0.2, a_n=22.$
We have to find $n$.
$$22=10+0.2(n-1)=10-0.2+0.2n=9.8+0.2n$$
$$22-9.8=0.2n$$
$$12.2=0.2n$$
$$n=61$$
