Question

What is the common difference of an arithmetic sequence defined by the formula an=6n+3?

Answer 1

The best way to solve this would be by the use of a table.

x) 1 2 3 4

y) 9 15 21 27

As you can see, the y value increases by 6 each time. Therefore d=6 or the common difference is 6

Answer 2

Hi,

$a_n=6n+3\\ a_{n+1}=6(n+1)+3\\\\a_{n+1}-a_n=6(n+1)+3-(6n+3)\\ =6n+6+3-6n-3\\ =6$