Exam 11: Sequences; Induction; the Binomial Theorem

Solve the problem. -A small business owner made $60,000 the first year he owned his store and made an additional 7% over the previous year in each subsequent year. Find how much he made during his fourth year of business. Find his Total earnings during the first four years. (Round to the nearest cent, if necessary.)

Determine whether the sequence is arithmetic. -2, -1, -4, -7, -10, ...

Write out the first five terms of the sequence. -{n - 2}

Use a graphing utility to find the sum of each sequence. -{ 3.4n + 8.75}, n=10

Find the first term, the common difference, and give a recursive formula for the arithmetic sequence. -8 th term is $62 ; 13$ th term is 42

An arithmetic sequence is given. Find the common difference and write out the first four terms. -{3n + 2}

Evaluate the expression. - $\left( \begin{array} { l } 6 \\0\end{array} \right)$

Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the sequence with the given first term, a1, and common ratio, r. -Find a9 when $a _ { 1 } = 4 , r = 2$

Use a graphing utility to find the sum of the geometric sequence. Round answer to two decimal places, if necessary. - $\sum _ { k = 1 } ^ { 5 } 4 ( 3 ) ^ { k }$

Express the sum using summation notation. - $3 + 12 + 27 + \ldots + 75$

Write out the sum. Do not evaluate. - $\sum _ { k = 1 } ^ { 5 } \frac { k + 1 } { k + 2 }$

Solve the problem. -A particular substance decays in such a way that it loses half its weight each day. How much of the substance is left after 7 days if it starts out at 16 grams?

Find the sum of the sequence. - $\sum _ { k = 1 } ^ { 4 } ( - 1 ) ^ { k } ( k + 6 )$

Find the fifth term and the nth term of the geometric sequence whose initial term, a, and common ratio, r, are given. - $a = \sqrt { 5 } ; r = \sqrt { 5 }$

Find the indicated coefficient or term. -The 5th term in the expansion of ( $( 2 x + 5 ) ^ { 5 }$

Write out the first five terms of the sequence. - $\left\{ \frac { n } { n ^ { 2 } + 2 } \right\}$

Find the sum of the sequence. - $\sum _ { k = 1 } ^ { 4 } ( - 1 ) ^ { k \cdot - 8 k }$

Evaluate the factorial expression. - $\frac { 7 ! } { 5 ! 2 ! }$

Find the indicated term using the given information. - $a _ { 18 } = 87 , a _ { 20 } = 99 ; a _ { 6 }$

Solve the problem. -Use the Binomial Theorem to approximate $( 1.01 ) ^ { 5 } = \left( 1 + 10 ^ { - 2 } \right) ^ { 5 }$ to 7 decimal places.