Exam 14: Sequences, Series, and the Binomial Theorem

Fill in the blank with one of the words or phrases listed below. general term common difference finite sequence common ratio Pascal's triangle infinite sequence factorial of series geometric sequence arithmetic sequence -The sum of the terms of a sequence is called a(n) --------.

Solve the problem. -A bicycle wheel rotates 400 times in a minute as long as the rider is pedalling. If the rider stops pedalling, the wheel starts to slow down. Each minute it will rotate only $3 / 4$ as many times as in the preceding minute. How many times will the wheel rotate in the 4 th minute after the rider's feet leave the pedals? Round your answer to the nearest unit.

Find the partial sum of the given sequence. - $\sum _ { i = 3 } ^ { 5 } 2 ( 3 ) ^ { i } ( - 1 ) ^ { i - 1}$

Solve the problem. -Find the sum of the first ten terms of the sequence $- 6 , - 1,4,9 , \ldots , 39$ where 39 is the tenth term.

Given are the first three terms of a sequence that is arithmetic. Find a1 and d. - $m , m - 12 , m - 24$

Use the binomial formula to expand the binomial. - $( 4 x - 2 ) ^ { 4 }$

Find the partial sum of the given sequence. - $\sum _ { i = 2 } ^ { 4 } i ( i - 5 )$

Write the series with summation notation. - $36 + 27 + 18 + 9 + 0 + ( - 9 )$

Evaluate the expression. - $\sum _ { i = 2 } ^ { 5 } \frac { - 6 } { i }$

Find the indicated term for the sequence whose general term is given. - $a _ { n } = 4 - n ^ { 2 } ; a _ { 7 }$

Evaluate the expression. - $\frac { 4 ! } { 2 ! 2 ! }$

Use Pascal's triangle to expand the binomial. - $( c + d ) ^ { 6 }$

Find the partial sum of the given sequence. - $\mathrm { S } _ { \infty }$ of the sequence $\mathrm { a } _ { 1 } = 13 , \mathrm { r } = \frac { 1 } { 3 }$

Find the indicated term of the sequence. -If the second term of an arithmetic progression is $- 6$ and the twelfth term is 84 , find the nineteenth term.

Fill in the blank with one of the words or phrases listed below. general term common difference finite sequence common ratio Pascal's triangle infinite sequence factorial of series geometric sequence arithmetic sequence -A(n) -----------is a function whose domain is the set of natural numbers.

Use the partial sum formula to find the partial sum of the given geometric sequence. -Find the sum of the first six terms of the geometric sequence $- 2 , - 8 , - 32 , \ldots$ .

Solve the problem. -On a gambling boat, Gertrude doubled her bet each time she won. If her first winning bet was $3 and she won six consecutive bets, find how much she won on the sixth bet. Find the total amount She won on these six bets.

Find the indicated term of the sequence. -The twelfth term of the arithmetic sequence $0,9,18 , \ldots$

. Write the word or phrase that best completes each statement or answers the question. -Initially, a pendulum swings through an arc of 3 feet. On each successive swing, the length of the arc is 0.8 of the previous length. After 10 swings, what total length will the pendulum have swung (to the nearest tenth of a foot)?

Solve the problem. -The population size of a culture of bacteria triples every day such that its size is modeled by the sequence $\mathrm { a } _ { \mathrm { n } } = 20 ( 3 ) ^ { \mathrm { n } - 1 }$ , where $\mathrm { n }$ is the number of the day just beginning. Find the size of the culture at the beginning of the third day and the size of the culture originally.