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 nth term of a sequence an is called the -----------

Given are the first three terms of a sequence that is arithmetic. Find a1 and d. - $2 , \frac { 3 } { 2 } , 1$

Find the indicated term. -The third term of the expansion of $( 3 x + 5 ) ^ { 3 }$

Write the first five terms of the sequence whose general term is given. - $a _ { n } = \frac { 4 } { n ^ { 2 } }$

Write the series with summation notation. - $14 + 23 + 32 + 41$

Find the indicated term. -The third term of the expansion of $( 5 x + 2 ) ^ { 3 }$

Solve the problem. -As Sunee improves her algebra skills, she takes 0.8 times as long to complete each homework assignment as she took to complete the preceeding assignment. If it took her 50 minutes to Complete her first assignment, find how long it took her to complete the fifth assignment. Find the Total time she took to complete her first five homework assignments. Round to the nearest minute.

Solve the problem. -In a game of chance, 12 cards numbered 1 to 12 are placed face down. The player who wins a card receives as many points as the number on the card. Player A wins cards 1 to 6 , and player B wins the remainder of the cards. Use an arithmetic series to find each player's score.

Given are the first three terms of a sequence that is geometric. Find a1 and r. - $1 , - 3,9$

Given are the first three terms of a sequence that is geometric. Find a1 and r. - $\frac { 3 } { 1 } , \frac { 3 } { 4 } , \frac { 3 } { 16 }$

Find the indicated term of the sequence. -The sixth term of the geometric sequence $\frac { 1 } { 9 } , \frac { 5 } { 9 } , \frac { 25 } { 9 } , \ldots$

Solve the problem. -The amount of decay in kilograms of a radioactive isotope each month is given by the sequence whose general term is $\mathrm { a } _ { \mathrm { n } } = 100 ( 0.2 ) ^ { \mathrm { n } }$ , where $\mathrm { n }$ is the number of the month. Find the amount of decay in the third month, and find the total amount of decay in the first three months. Round to the nearest tenth, if necessary.

Use Pascal's triangle to expand the binomial. - $( s + t ) ^ { 3 }$

Find the indicated term. -The fourth term of the expansion of $( s - t ) ^ { 12 }$

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 triangular array of the coefficients of the terms of the expansion of (a + b)ⁿ is called ------------.

Find the sum of the terms of the infinite geometric sequence. - $- 20 , - 5 , - \frac { 5 } { 4 } , \cdots$

Use the binomial formula to expand the binomial. - $( 4 x - 5 y ) ^ { 3 }$

Write the first five terms of the arithmetic sequence whose first term, a1, and common difference, d, are given. - $a _ { 1 } = 1 ; d = 4$

Solve the problem. -A custodian set up chairs for a lecture. There are 9 chairs in the first row, 14 chairs in the second row, 19 chairs in the third, and so on for 8 rows. Write the sequence that describes the number of chairs in each row. Find the total number of chairs set up for the lecture.

Given are the first three terms of a sequence that is geometric. Find a1 and r. - $\frac { 2 } { 3 } , \frac { 8 } { 3 } , \frac { 32 } { 3 }$