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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 1346 pages

ISBN: 9780998625720

Chapter 12: Q. 12.9 (page 1167)

Find a general term for the sequence whose first five terms are shown. −3, 9, −27, 81, −243, ...

Short Answer

Expert verified

The general term for the given sequence is $a_{n} = {(- 1)}^{n} 3^{n}$

Step by step solution

01

Step 1. Given information

The first five terms are shown. −3, 9, −27, 81, −243,...

02

Step 2. Observing the pattern

$\begin{array}{l} n & 1 & 2 & 3 & 4 & 5 & ... & n \\ Terms & - 3 & 9 & - 27 & 81 & - 243 & ... \\ Pattern & {(- 1)}^{1} 3^{1} & {(- 1)}^{2} 3^{2} & {(- 1)}^{3} 3^{3} & {(- 1)}^{4} 3^{4} & {(- 1)}^{5} 3^{5} & ... & {(- 1)}^{n} 3^{n} \end{array}$

03

Step 3. Conclusion

The numbers are powers of 3. The signs are alternating, with odd $n$ negative.

Therefore,

The general term islocalid="1645103689408" $a_{n} = {(- 1)}^{n} 3^{n}$

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Most popular questions from this chapter

In the following exercises, write the first five terms of each geometric sequence with the given first term and common ratio.

$a_{1} = 64$ and $r = \frac{1}{4}$

Write the first five terms of the sequence whose general term is $a_{n} = 2 n - 5$

Write each sum using summation notation: −2 + 4 − 6 + 8 − 10.

In the following exercises, expand each binomial using Pascal's Triangle.

$(x + 4)^{4}$

Write the sum using summation notation: $1 + \frac{1}{4} + \frac{1}{9} + \frac{1}{16} + \frac{1}{25}$ .

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