Question

The first term of an arithmetic sequence is -5, and the tenth term is 13. Find the common difference.

Answer 1

well you can use the formula

\[13 = -5 + (10 - 1) \times d\]
just solve for d

Answer 2

\[a_n = a_1 + (n-1)d\]where

\(n\) is the number of the term you want,
\(a_n\) is the value of the term you want,
\(d\) is the common difference, and
\(a_1\) is the first term in the sequence

As you can see, my distinguished colleague has already "filled in the blanks" for you...