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Chapter 8: Problem 5

Write the first four terms of each sequence whose general term is given. $$a_{n}=(-3)^{n}$$

Short Answer

Expert verified
The first four terms of the sequence are -3, 9, -27, 81.

Step by step solution

01

Substitute n=1

The first term can be found by substituting \(n=1\) into the formula. That results in: \(a_1= (-3)^1 = -3\)
02

Substitute n=2

The second term can be found by substituting \(n=2\) into the formula. This results in: \(a_2= (-3)^2 = 9\)
03

Substitute n=3

The third term is found by substituting \(n=3\) into the formula. This results in: \(a_3= (-3)^3 = -27\)
04

Substitute n=4

The fourth term is found by substituting \(n=4\) into the formula. This results in: \(a_4= (-3)^4 = 81\)

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Most popular questions from this chapter

Write the first three terms in each binomial expansion, expressing the result in simplified form. $$ (x+2)^{8} $$

Write the first three terms in each binomial expansion, expressing the result in simplified form. $$ \left(x^{2}+1\right)^{16} $$

Use the Binomial Theorem to expand and then simplify the result: \(\left(x^{2}+x+1\right)^{3}\). [ Hint: Write \(x^{2}+x+1\) as \(\left.x^{2}+(x+1)\right]\)

Find the term indicated in each expansion. \(\left(x^{2}+y^{3}\right)^{8} ;\) sixth term

Use the Binomial Theorem to expand each binomial and express the result in simplified form. $$ (x-2)^{5} $$
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