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Chapter 14: 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

01

Substituting n=1

For the first term, substitute \(n=1\) into the sequence formula \(a_{n}=(-1)^{n+1}(n+4)\). This gives \(a_{1}=(-1)^{1+1}(1+4)\), which evaluates to \(a_{1}=5\).
02

Substituting n=2

For the second term, substitute \(n=2\) into the sequence formula. This gives \(a_{2}=(-1)^{2+1}(2+4)\), which evaluates to \(a_{2}=-6\).
03

Substituting n=3

For the third term, substitute \(n=3\) into the sequence formula. This gives \(a_{3}=(-1)^{3+1}(3+4)\), which evaluates to \(a_{3}=7\).
04

Substituting n=4

For the fourth term, substitute \(n=4\) into the sequence formula. This gives \(a_{4}=(-1)^{4+1}(4+4)\), which evaluates to \(a_{4}=-8\).

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Most popular questions from this chapter

Use the Binomial Theorem to find a polynomial expansion for each function. Then use a graphing utility and an approach similar to the one in Exercises 69 and 70 to verify the expansion. $$f_{1}(x)=(x-2)^{4}$$

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Find a general term, \(a_{n},\) for each sequence. More than one answer may be possible. Evaluate without using a calculator: \(\frac{600 !}{599 !}\)
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