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Chapter 5: Problem 98

Write a formula for the general term (the nth term) of each geometric sequence. Then use the formula for \(a_{n}\) to find \(a_{7}\), the seventh term of the sequence. \(0.0007,-0.007,0.07,-0.7, \ldots\)

Short Answer

Expert verified
The formula for the general term of the sequence is \(a_{n} = 0.0007 * (-10)^{n-1}\) and the seventh term of the sequence \(a_{7}\) is -700.

Step by step solution

01

Identify the first term(a1) and the common ratio(r)

The first term \(a_{1}\) of the sequence is 0.0007 and the common ratio \(r\) can be found by dividing the second term by the first term. That is \(r = -0.007 / 0.0007 = -10\)
02

Write down the general term

Using the general formula for the nth term of a geometric sequence, the general term \(a_n\) is described as \(a_{n} = a_{1} * r^{n-1} \). Substituting \(a_{1}\) as 0.0007 and \(r\) as -10, the formula for the general term of the sequence is \(a_{n} = 0.0007 * (-10)^{n-1}\)
03

Find the seventh term of the sequence

To find the seventh term of the sequence, use the general term equation and replace n with 7. This leads to \(a_{7} = 0.0007 * (-10)^{7-1} = 0.0007 * (-10)^6 = -700\).

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Most popular questions from this chapter

Find the indicated term for the geometric sequence with first term, \(a_{1}\), and common ratio, \(r\). Find \(a_{20}\), when \(a_{1}=2, r=2\).

Write a formula for the general term (the nth term) of each arithmetic sequence. Then use the formula for \(a_{n}\) to find \(a_{20}\), the 20 th term of the sequence. \(2,7,12,17, \ldots\)

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Find the indicated term for the geometric sequence with first term, \(a_{1}\), and common ratio, \(r\). Find \(a_{8}\), when \(a_{1}=6, r=\frac{1}{2}\).
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