Chapter 12: Q 35. (page 825)

In Problems 31–38, find the nth term $a_{n}$ of each geometric sequence. When given, r is the common ratio.
$a_{6} = 243; r = - 3$

Short Answer

Expert verified

The $a_{1} i s - 1 a n d a_{n} = - 1 \cdot {(- 3)}^{n - 1}$

Step by step solution

Step 1. Write the given information

The common ratio is $r = - 3 a n d a_{6} = 243$

Step 2. Find the a1 and nth term.

The formula for the nth terms is: $a_{n} = a_{1} \cdot r^{n - 1}$

localid="1646971157096" $a_{6} = a_{1} \cdot {(- 3)}^{6 - 1} 243 = a_{1} \cdot {(- 3)}^{5} 243 = a_{1} \cdot {(- 3)}^{5} a_{1} = - 1$

localid="1646971172213" $a_{n} = - 1 \cdot {(- 3)}^{n - 1} = - 1 \cdot {(- 3)}^{n - 1}$

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In Problems 31–38, find the nth term $a_{n}$ of each geometric sequence. When given, r is the common ratio.
$a_{6} = 243; r = - 3$

Short Answer

Step by step solution

Step 1. Write the given information

Step 2. Find the a1 and nth term.

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In Problems 31–38, find the nth term anof each geometric sequence. When given, r is the common ratio.a6=243;r=-3

Short Answer

Step by step solution

Step 1. Write the given information

Step 2. Find the a1 and nth term.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Calculus

Probability and Statistics

Discrete Mathematics

Statistics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

In Problems 31–38, find the nth term $a_{n}$ of each geometric sequence. When given, r is the common ratio.
$a_{6} = 243; r = - 3$