91Ó°ÊÓ

Find the first five terms of the given recursively defined sequence. \(a_{n}=\frac{1}{1+a_{n-1}} \quad\) and \(\quad a_{1}=1\)

Show that \(n^{2}-n+41\) is odd for all natural numbers \(n.\)

9–16 Determine whether the sequence is arithmetic. If it is arithmetic, find the common difference. $$2.6,4.3,6.0,7.7, \ldots$$

\(13-20=\) Evaluate the expression. $$ \left(\begin{array}{c}{100} \\ {98}\end{array}\right) $$

Find the first five terms of the given recursively defined sequence. \(a_{n}=a_{n-1}+a_{n-2} \quad\) and \(\quad a_{1}=1, a_{2}=2\)

Mortgage A couple secures a 30 -year loan of \(\$ 100,000\) at 9\(\frac{3}{4} \%\) per year, compounded monthly, to buy a house. (a) What is the amount of their monthly payment? (b) What total amount will they pay over the 30 -year period? (c) If, instead of taking the loan, the couple deposits the monthly payments in an account that pays 9\(\frac{3}{4} \%\) interest per year, compounded monthly, how much will be in the account at the end of the 30 -year period?

Determine whether the sequence is geometric. If it is geometric, find the common ratio. $$ 1.0,1.1,1.21,1.331, \dots $$

9–16 Determine whether the sequence is arithmetic. If it is arithmetic, find the common difference. $$\frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \frac{1}{5}, \dots$$

Find the first five terms of the given recursively defined sequence. \(a_{n}=a_{n-1}+a_{n-2}+a_{n-3} \quad\) and \(\quad a_{1}=a_{2}=a_{3}=1\)

Determine whether the sequence is geometric. If it is geometric, find the common ratio. $$ \frac{1}{2}, \frac{1}{4}, \frac{1}{6}, \frac{1}{8}, \dots $$