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Chapter 5: Problem 10
Use properties of exponents to simplify each expression. First express the answer in exponential form. Then evaluate the expression. \(\frac{6^{7}}{6^{5}}\)
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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. \(12,6,3, \frac{3}{2}, \ldots\)
Write the first six terms of the geometric sequence with the first term, \(a_{1}\), and common ratio, \(r\). \(a_{1}=2, r=-3\)
Determine whether each sequence is arithmetic or geometric. Then find the next two terms. \(7,-7,-21,-35, \ldots\)
Find the indicated term for the geometric sequence with first term, \(a_{1}\), and common ratio, \(r\). Find \(a_{30}\), when \(a_{1}=8000, r=-\frac{1}{2}\).
Find the indicated term for the geometric sequence with first term, \(a_{1}\), and common ratio, \(r\). Find \(a_{6}\), when \(a_{1}=-2, r=-3\).
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