Problem 8 Write the first four terms of ea... [FREE SOLUTION]

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College Algebra

Robert Blitzer

$Math Studyset 91影视 Explanations$ Math

3 Edition

Chapter 8: Problem 8

Write the first four terms of each sequence whose general term is given. $$a_{n}=(-1)^{n+1}(n+4)$$

Short Answer

Expert verified

The first four terms of the sequence are 5, -6, 7, -8.

Step by step solution

Identify and Understand the General Term

The given general term is $a_{n}=(-1)^{n+1}(n+4)$. It suggests that each term is given by multiplying a positive or negative value based on whether $n+1$ is even or odd, with the equation $n+4$.

Determine the First Term ($a_{1}$)

We substitute $n=1$ into the general term $a_{n}=(-1)^{n+1}(n+4)$, which yields $a_{1}=(-1)^{1+1}(1+4) = (-1)^2(5) = 5$. So, the first term of the sequence is 5.

Determine the Second Term ($a_{2}$)

Substitute $n=2$ into the general term. This gives us $a_{2}=(-1)^{2+1}(2+4) = -(-1)^3(6) = -6$. So, the second term of the sequence is -6.

Determine the Third Term ($a_{3}$)

Substitute $n=3$ into the general term, which yields $a_{3}=(-1)^{3+1}(3+4) = (-1)^4(7) = 7$. So, the third term of the sequence is 7.

Determine the Fourth Term ($a_{4}$)

Substitute $n=4$ into the general term, leading us to $a_{4}=(-1)^{4+1}(4+4) = -(-1)^5(8) = -8$. So, the fourth term of the sequence is -8.

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91影视

Write the first four terms of each sequence whose general term is given. $$a_{n}=(-1)^{n+1}(n+4)$$

Short Answer

Step by step solution

Identify and Understand the General Term

Determine the First Term (\(a_{1}\))

Determine the Second Term (\(a_{2}\))

Determine the Third Term (\(a_{3}\))

Determine the Fourth Term (\(a_{4}\))

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