Chapter 12: Q 4. (page 824)
True or False: A geometric sequence may be defined recursively.
The statement a geometric sequence may be defined recursively is true.
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Roth IRA On January 1, 1999, Bob decided to place \(500 at the end of each quarter into a Roth Individual Retirement Account.
(a) Find a recursive formula that represents Bob’s balance at the end of each quarter if the rate of return is assumed to be 8% per annum compounded quarterly.
(b) How long will it be before the value of the account exceeds \)100,000?
(c) What will be the value of the account in 25 years when Bob retires?
In Problems 51–66, determine whether each infinite geometric series converges or diverges. If it converges, find its sum.
In Problems 11–16, evaluate each factorial expression.
Fibonacci Sequence: Let
define the nth term of a sequence.
(a) Show that u1= 1 and u2 = 1.
(b) Show that un+2 = un+1 + un.
(c) Draw the conclusion that {un} is the Fibonacci sequence.
In Problems 71-82, find the sum of each sequence.
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