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Exercises Sequences, counting and probability

Example 6 from Algebra and Trigonometry, 13.2 Arithmetic Sequences

Finding the Number of Terms in a Finite Arithmetic Sequence

Find the number of terms in the finite arithmetic sequence.

{8, 1, –6, ..., –41}

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 common difference can be found by subtracting the first term from the second term.
$1 - 8 = - 7$

The common difference is $- 7$ . Substitute the common difference and the initial term of the sequence into the $n th$ term formula and simplify.
$\begin{array}{l} a_{n} = a_{1} + d (n - 1) \\ a_{n} = 8 + (- 7) (n - 1) \\ a_{n} = 15 - 7 n \end{array}$
Substitute $- 41$ for $a_{n}$ and solve for $n$
$\begin{array}{l} - 41 = 15 - 7 n \\ 8 = n \end{array}$
There are eight terms in the sequence.

Your turn

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

Find the number of terms in the finite arithmetic sequence.

{6, 11, 16, ..., 56}

How did it go?

PreviousWriting the nth Term Explicit Formula for an Arithmetic Sequence Next Solving Application Problems with Arithmetic Sequences

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.