91Ó°ÊÓ

Use mathematical induction to prove that the formula is true for all natural numbers n. $$1+4+7+\cdots+(3 n-2)=\frac{n(3 n-1)}{2}$$

\(1-12\) . Use Pascal's triangle to expand the expression. $$ (2 x+1)^{4} $$

1–4 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). $$a_{n}=\frac{5}{2}-(n-1)$$

Use mathematical induction to prove that the formula is true for all natural numbers n. $$5+8+11+\cdots+(3 n+2)=\frac{n(3 n+7)}{2}$$

\(1-12\) . Use Pascal's triangle to expand the expression. $$ \left(x+\frac{1}{x}\right)^{4} $$

Annuity 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.

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). $$ a_{n}=\frac{5}{2}\left(-\frac{1}{2}\right)^{n-1} $$

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

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). $$ a_{n}=\frac{5}{2}\left(-\frac{1}{2}\right)^{n-1} $$

Annuity 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.