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Chapter 8: Problem 1

Write the first six terms of each arithmetic sequence. $$a_{1}=200, d=20$$

Short Answer

Expert verified
The first six terms of the arithmetic sequence are 200, 220, 240, 260, 280, 300.

Step by step solution

01

Find the first term

The first term, \(a_1\) is given as 200. Therefore, the first term of the sequence is 200.
02

Calculate the second term

To calculate the second term, we apply the formula \(a_n = a_1 + (n - 1) * d\). With \(n = 2\), \(a_1 = 200\), and \(d = 20\), we find \(a_2 = 200 +(2-1)*20 = 220\)
03

Calculate the third term

With \(n = 3\), \(a_1 = 200\), and \(d = 20\), we find \(a_3 = 200 +(3-1)*20 = 240\)
04

Calculate the fourth term

With \(n = 4\), \(a_1 = 200\), and \(d = 20\), we find \(a_4 = 200 +(4-1)*20 = 260\)
05

Calculate the fifth term

With \(n = 5\), \(a_1 = 200\), and \(d = 20\), we find \(a_5 = 200 +(5-1)*20 = 280\)
06

Calculate the sixth term

With \(n = 6\), \(a_1 = 200\), and \(d = 20\), we find \(a_6 = 200 +(6-1)*20 = 300\)

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Most popular questions from this chapter

Graph each of the functions in the same viewing rectangle. Describe how the graphs illustrate the Binomial Theorem. $$ \begin{array}{l}f_{1}(x)=(x+2)^{3} \\\f_{2}(x)=x^{3} \\\f_{3}(x)=x^{3}+6 x^{2} \\\f_{4}(x)=x^{3}+6 x^{2}+12 x \\\f_{5}(x)=x^{3}+6 x^{2}+12 x+8\end{array} $$ Use a \([-10,10,1]\) by \([-30,30,10]\) viewing rectangle.

Evaluate the given binomial coefficient. $$ \left(\begin{array}{l}8 \\\3\end{array}\right) $$

Use the Binomial Theorem to expand each binomial and express the result in simplified form. $$ (x+2)^{3} $$

Explain how to evaluate \(\left(\begin{array}{l}n \\ r\end{array}\right) .\) Provide an example with your explanation.

Use the Binomial Theorem to expand each binomial and express the result in simplified form. $$ (x+3 y)^{3} $$
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