Exam 11: Sequences; Induction; the Binomial Theorem

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 a 9 when $\mathrm { a } _ { 1 } = 4 , \mathrm { r } = 2$ .

Write the word or phrase that best completes each statement or answers the question. - $\text { Use the Binomial Theorem to approximate } ( 1.01 ) ^ { 5 } = \left( 1 + 10 ^ { - 2 } \right) ^ { 5 } \text { to } 7 \text { decimal places. }$

Express the sum using summation notation. - $\frac { 1 } { 4 } + \frac { 2 } { 5 } + \frac { 1 } { 2 } + \cdots + \frac { 4 } { 5 }$

Expand the expression using the Binomial Theorem. - $( 2 x + 1 ) ^ { 5 }$

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

Find the sum of the arithmetic sequence. -6 + 12 + 18 + ... + 876

Solve. -A town has a population of 20,000 people and is increasing by $10 \%$ every year. What will the population be at the end of 4 years?

Choose the one alternative that best completes the statement or answers the question. Evaluate the expression. - $\left( \begin{array} { c } 263 \\ 3 \end{array} \right)$

Choose the one alternative that best completes the statement or answers the question. -A new piece of equipment cost a company $54,000. Each year, for tax purposes, the company depreciates the value by 25%.What value should the company give the equipment after 8 years?

Expand the expression using the Binomial Theorem. - $( 5 x + 2 ) ^ { 4 }$

Use a graphing utility to find the sum of the geometric sequence. Round answer to two decimal places, if necessary. - $2 - 6 + 18 - 54 + 162 - \cdots + 2 \cdot ( - 3 ) ^ { 11 }$

Find the indicated term using the given information. -a = 3 , d = 3 ; a23

Find the indicated term of the sequence. -The ninth term of the arithmetic sequence $- 14 \sqrt { 3 } , - 9 \sqrt { 3 } , - 4 \sqrt { 3 } , \ldots$

Find the nth term of the geometric sequence. - $6,18,54,162,486$

Find the sum of the arithmetic sequence. -{2n - 2}, n = 43

Find the sum of the sequence. - $\sum _ { k = 3 } ^ { 5 } \left( k ^ { 2 } - 9 \right)$

Choose the one alternative that best completes the statement or answers the question. -A ping-pong ball is dropped from a height of 9 ft and always rebounds 13 of the distance fallen. Find the total sum of the rebound heights of the ball.

Solve. -During a five-year period, a company doubles its profits each year. If the profits at the end of the fifth year are $\$$ 192,000 , then what are the profits for each of the first four years?

Write the word or phrase that best completes each statement or answers the question. - $\text { Use the Binomial Theorem to approximate } ( 0.98 ) ^ { 6 } = \left( 1 - 2 \left( 10 ^ { - 2 } \right) \right) ^ { 6 } \text { to } 5 \text { decimal places. }$

Determine whether the sequence is arithmetic. - $4,12,36,108,972 , \ldots$