Question

The first term of an arithmetic sequence is-3 and the 15 term is 53. What is the common difference of the sequence?

Answer 1

$a_2=a_1+d$
$a_3=a_2+d=a_1+2d$
$a_4=a_3+d=a_1+3d$
...
$a_{15}=a_1+14d$

Since $a_1=-3$ and $a_{15}=53$, the common difference $d$ is

$53=-3+14d\implies d=4$