Exam 11: Sequences, Induction, and Probability

Write a formula for the general term (the nth term) of the geometric sequence. - $\frac { 1 } { 9 } , - \frac { 1 } { 18 } , \frac { 1 } { 36 } , - \frac { 1 } { 72 } , \ldots$

Use the Formula for the General Term of an Arithmetic Sequence Choose the one alternative that best completes the statement or answers the question. Use the formula for the general term (the nth term) of an arithmetic sequence to find the indicated term of the sequence with the given first term, a1, and common difference, d. -Find a 19 when $a _ { 1 } = - 4 , d = - \frac { 5 } { 3 }$ .

Write the word or phrase that best completes each statement or answers the question. Use mathematical induction to prove that the statement is true for every positive integer n. - $1 + 4 + 7 + \ldots + ( 3 n - 2 ) = \frac { n ( 3 n - 1 ) } { 2 }$

Express the sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation. - $5 ^ { 2 } + 10 ^ { 3 } + 15 ^ { 4 } + \ldots + 40 ^ { 9 }$

Write a formula for the general term (the nth term) of the arithmetic sequence. Then use the formula for $\mathbf { a } _ { \mathbf { n } }$ to find $a _ { 20 }$ , the 20th term of the sequence. -Jacie is considering a job that offers a monthly starting salary of $3000 and guarantees her a monthly raise of $190 during her first year on the job. Find the general term of this arithmetic sequence and her monthly salary at the end of her first year.

Use the Permutations Formula -A church has 9 bells in its bell tower. Before each church service 5 bells are rung in sequence. No bell is rung more than once. How many sequences are there?

Use the Formula for the Sum of the First n Terms of a Geometric Sequence -Find the sum of the first 11 terms of the geometric sequence: $\frac { 1 } { 2 } , 1,2,4,8 , \ldots$

Use the Permutations Formula - ${ } _ { 8 } \mathrm { P } _ { 3 }$

Find the term indicated in the expansion. - $\left( x ^ { 4 } + y ^ { 2 } \right) ^ { 7 } ; 4$ th term

Use the Formula for the Sum of the First n Terms of a Geometric Sequence -Find the sum of the first five terms of the geometric sequence: -2, -6, -18, . . . .

Expand a Binomial Raised to a Power - $( 4 x + 3 ) ^ { 3 }$

Use the Formula for the Sum of the First n Terms of a Geometric Sequence -Find the sum of the first 11 terms of the geometric sequence: -7, -14, -28, -56, -112, . . . .

Find the indicated sum. Use the formula for the sum of the first n terms of a geometric sequence. -As Sunee improves her algebra skills, she takes 0.9 times as long to complete each homework assignment as she took to complete the preceeding assignment. If it took her 60 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.)

The general term of a sequence is given. Determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio. -A football player signs a contract with a starting salary of $860,000 per year and an annual increase of 5.5% beginning in the second year. What will the athlete's salary be, to the nearest dollar, in the sixth year?

Use Summation Notation - $\sum _ { \mathrm { i } = 1 } ^ { 5 } \frac { ( - 1 ) ^ { \mathrm { i } + 1 } } { ( \mathrm { i } + 1 ) ! }$

Use the Formula for the Sum of an Infinite Geometric Series - $3 - 1 + \frac { 1 } { 3 } - \frac { 1 } { 9 } + \ldots$

Write a formula for the general term (the nth term) of the arithmetic sequence. Then use the formula for $\mathbf { a } _ { \mathbf { n } }$ to find $a _ { 20 }$ , the 20th term of the sequence. - $21,12,3 , - 6 , \ldots$

Additional Concepts - $\frac { 9 ^ { P _ { 3 } } } { 3 ! } - 9 C _ { 3 }$

Use Summation Notation - $\sum _ { i = 1 } ^ { 4 } \frac { 1 } { 8 i }$

Compute Theoretical Probability -A bag contains 7 red marbles, 2 blue marbles, and 1 green marble. What is the probability of choosing a marble that is not blue when one marble is drawn from the bag?