Arithmetic Sequences I

Problem 220: Consider the sequence $8, 15, 22, 29, 36, \dots$ . Find

a. the common difference and

b. the next five terms of the sequence.

Solution: This is an arithmetic sequence. A sequence of numbers that are connected by a common difference.

a. The common difference is 7 because

(1) $\begin{align*} 15 - 8 & = 7 \\ 22 - 15 & = 7 \\ 29 - 22 & = 7 \\ 36-29 & = 7.\end{align*}$

b. We can use the common difference to find as many terms as we want. That is, the next five terms are

(2) $\begin{align*}36 \mathbf{+ 7}& = 43 \\ 43 \mathbf{+ 7} & = 50 \\ 50 \mathbf{+ 7} & = 57 \\ 57 \mathbf{+ 7} & = 64 \\ 64 \mathbf{+ 7} & = 71. \end{align*}$

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