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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 1346 pages

ISBN: 9780998625720

Chapter 11: Q. 12.8 (page 1069)

Find a general term for the sequence whose first five terms are shown. 5, 10, 15, 20, 25, …

Short Answer

Expert verified

The general term for the given sequence is $a_{n} = 5 n .$

Step by step solution

01

Step 1, Given information

The first five terms of the sequence are 5, 10, 15, 20, 25,...

02

Step 2. Observing the pattern

$\begin{array}{l} n & 1 & 2 & 3 & 4 & 5 & ... & n \\ Terms & 5 & 10 & 15 & 20 & 25 & ... \\ Pattern & 5 (1) & 5 (2) & 5 (3) & 5 (4) & 5 (5) & ... & 5 (n) \end{array}$

03

Step 3. Conclusion

From the above table, we can observe that all the numbers are multiple of 5.

Therefore, the general term for the given sequence is $a_{n} = 5 n .$

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Most popular questions from this chapter

Use the Quotient Property to Simplify Radical Expressions

In the following exercises, use the Quotient Property to simplify square roots.

$a . \sqrt{\frac{72}{98}} b . \sqrt[3]{\frac{24}{81}} c . \sqrt[4]{\frac{6}{96}}$

Multiply $\frac{3 {xy}^{2}}{8 y^{3}} . \frac{16 y^{2}}{24 x}$

Simplify the rational expression $\frac{20 - 5 y}{y^{2} - 16}$

Simplify $\sqrt{48}$ .

Of all the factoring methods covered in this chapter (GCF, grouping, undo FOIL, 'ac' method, special products) which is the easiest for you? Which is the hardest? Explain your answers.

See all solutions

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