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`