The term of an arithmetic sequence is - 5 and the tenth term is 13 find the common difference

nth term of an arithmetic sequence:

The nth term of an arithmetic sequence is.

Where is the first term and d is the common difference.

The initial term is and common difference is.

The nth term of an arithmetic sequence is.

Substitute and in above equation.

The nth term of an arithmetic sequence is

Substitute in

The fifty-first term of an arithmetic sequence is

Solution:

The nth term of an arithmetic sequence is

The fifty-first term of an arithmetic sequence is

D=2

13 - - 5=18

There are 9 positions between - 5 and 13.

18/9=2

D=2