11. Write the formula for the nth term of the following sequence: 3,-9, 27,-81, 243, -..

Calculus: Early Transcendentals
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ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Question 11: Write the formula for the nth term of the following sequence: 3, -9, 27, -81, 243, ...**

The sequence provided is an alternating geometric sequence. To derive the formula for the nth term, observe the pattern in the sequence. The first term is 3, and each subsequent term is obtained by multiplying the previous term by -3.

Therefore, the nth term \(a_n\) of the sequence can be expressed using the formula:

\[ a_n = 3 \times (-3)^{n-1} \]

This formula will allow you to find any term in the sequence by substituting the position of the term (n) into the formula.

For example:
- To find the first term (\(a_1\)):
  \[ a_1 = 3 \times (-3)^{1-1} = 3 \times 1 = 3 \]
- To find the second term (\(a_2\)):
  \[ a_2 = 3 \times (-3)^{2-1} = 3 \times (-3) = -9 \]

By examining the common ratio and the signs of the terms, it can be confirmed that the sequence will alternate in sign and increase in magnitude as specified by the formula.
Transcribed Image Text:**Question 11: Write the formula for the nth term of the following sequence: 3, -9, 27, -81, 243, ...** The sequence provided is an alternating geometric sequence. To derive the formula for the nth term, observe the pattern in the sequence. The first term is 3, and each subsequent term is obtained by multiplying the previous term by -3. Therefore, the nth term \(a_n\) of the sequence can be expressed using the formula: \[ a_n = 3 \times (-3)^{n-1} \] This formula will allow you to find any term in the sequence by substituting the position of the term (n) into the formula. For example: - To find the first term (\(a_1\)): \[ a_1 = 3 \times (-3)^{1-1} = 3 \times 1 = 3 \] - To find the second term (\(a_2\)): \[ a_2 = 3 \times (-3)^{2-1} = 3 \times (-3) = -9 \] By examining the common ratio and the signs of the terms, it can be confirmed that the sequence will alternate in sign and increase in magnitude as specified by the formula.
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