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Chapter 5: Problem 78
Find the indicated term for the geometric sequence with first term, \(a_{1}\), and common ratio, \(r\). Find \(a_{4}\), when \(a_{1}=4, r=-3\).
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Determine whether each sequence is arithmetic or geometric. Then find the next two terms. \(6,-6,-18,-30, \ldots\)
Use the appropriate formula shown above to find \(2+4+6+8+\cdots+200\), the sum of the first 100 positive even integers.
Determine whether each statement makes sense or does not make sense, and explain your reasoning. There's no end to the number of geometric sequences that I can generate whose first term is 5 if I pick nonzero numbers \(r\) and multiply 5 by each value of \(r\) repeatedly.
A professional baseball player signs a contract with a beginning salary of $$\$ 3,000,000$$ for the first year with an annual increase of \(4 \%\) per year beginning in the second year. That is, beginning in year 2 , the athlete's salary will be \(1.04\) times what it was in the previous year. What is the athlete's salary for year 7 of the contract? Round to the nearest dollar.
Write the first six terms of the geometric sequence with the first term, \(a_{1}\), and common ratio, \(r\). \(a_{1}=\frac{1}{2}, r=2\)
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