91Ó°ÊÓ

The \(n\) th term of a sequence is given. (a) Find the first five terms of the sequence. (b) What is the common ratio \(r ?\) (c) Graph the terms you found in (a). $$a_{n}=5(2)^{n-1}$$

A sequence is given. (a) Find the first five terms of the sequence. (b) What is the common difference \(d ?\) (c) Graph the terms you found in (a). $$a_{n}=5+2(n-1)$$

Find the amount of an annuity that consists of 20 annual payments of \(\$ 5000\) each into an account that pays interest of \(12 \%\) per year.

Find the first four terms and the 100th term of the sequence. $$a_{n}=n^{2}+1$$

Find the amount of an annuity that consists of 20 semiannual payments of \(\$ 500\) each into an account that pays \(6 \%\) interest per year, compounded semiannually.

Use mathematical induction to prove that the formula is true for all natural numbers \(n\) $$1^{2}+2^{2}+3^{2}+\cdots+n^{2}=\frac{n(n+1)(2 n+1)}{6}$$

Use Pascal's triangle to expand the expression. $$(2 x+1)^{4}$$

The \(n\) th term of a sequence is given. (a) Find the first five terms of the sequence. (b) What is the common ratio \(r ?\) (c) Graph the terms you found in (a). $$a_{n}=3(-4)^{n-1}$$

A sequence is given. (a) Find the first five terms of the sequence. (b) What is the common difference \(d ?\) (c) Graph the terms you found in (a). $$a_{n}=3-4(n-1)$$

Find the first four terms and the 100th term of the sequence. $$a_{n}=\frac{(-1)^{n}}{n^{2}}$$