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Writing Terms of Arithmetic Sequences · Physics Playground

Exercises Sequences, counting and probability

Example 3 from Algebra and Trigonometry, 13.2 Arithmetic Sequences

Writing Terms of Arithmetic Sequences

Given $a_{1} = 8$ and $a_{4} = 14$ , find $a_{5}$ .

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
The sequence can be written in terms of the initial term 8 and the common difference $d$ .

${8, 8 + d, 8 + 2 d, 8 + 3 d}$
We know the fourth term equals 14; we know the fourth term has the form $a_{1} + 3 d = 8 + 3 d$ .
We can find the common difference $d$ .
$\begin{array}{l} a_{n} = a_{1} + (n - 1) d \\ a_{4} = a_{1} + 3 d \\ a_{4} = 8 + 3 d & Write the fourth term of the sequence in terms of a_{1} and d . \\ 14 = 8 + 3 d & Substitute 14 for a_{4} . \\ d = 2 & Solve for the common difference . \end{array}$
Find the fifth term by adding the common difference to the fourth term.
$a_{5} = a_{4} + 2 = 16$

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Given $a_{3} = 7$ and $a_{5} = 17$ , find $a_{2}$ .

How did it go?

PreviousWriting Terms of Arithmetic Sequences Next Writing a Recursive Formula for an Arithmetic Sequence

From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 13.2, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.