RIP Brilliant Community on July 2, 2021, Question 2

The $nth$ term of an Arithmetic Sequence is given by the formula

$a_n=a_m+(n-m)d$

Substitute to solve for $d$ .

$a_9=a_7+(9-7)d$

$19=15+(2)(d)$

$d=2$

So the $12th$ term is

$a_{12}=a_9+(12-9)(2)$

$a_{12}=19+(3)(2)$

$\boxed{a_{12}=25}$