Language

Loading…

Physics Playground

Built on open, peer-reviewed sources: OpenStax, The Feynman Lectures on Physics, HyperPhysics, NASA and NIST. See our sources.

Learn

Physics course
Math for Physics
Start with the math toolkit
Simulations
Glossary
Exercises
Past exams
Library
How we teach

Company

Pricing
Terms
Privacy
Contact

Writing an Explicit Formula for the n th Term of a Geometric Sequence · Physics Playground

Exercises Sequences, counting and probability

Example 5 from Algebra and Trigonometry, 13.3 Geometric Sequences

Writing an Explicit Formula for the n th Term of a Geometric Sequence

Write an explicit formula for the $n th$ term of the following geometric sequence.

{2, 10, 50, 250, ...}

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 first term is 2. The common ratio can be found by dividing the second term by the first term.

$\frac{10}{2} = 5$

The common ratio is 5. Substitute the common ratio and the first term of the sequence into the formula.

$\begin{array}{l} a_{n} = a_{1} r^{(n - 1)} \\ a_{n} = 2 \cdot 5^{n - 1} \end{array}$
The graph of this sequence in Figure 4 shows an exponential pattern.

Figure 4

Your turn

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

Write an explicit formula for the following geometric sequence.

{–1, 3, –9, 27, ...}

How did it go?

PreviousWriting Terms of Geometric Sequences Using the Explicit Formula Next Solving Application Problems with Geometric Sequences

From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 13.3, 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.

Solution

Your turn