Exam 11: Sequences, Induction, and Probability

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. - $1,5,9,13,17 , \ldots$

Geometric Sequences and Series 1 Find the Common Ratio of a Geometric Sequence - $4 , - 12,36 , - 108,324$

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. -To train for a race, Will begins by jogging 14 minutes one day per week. He increases his jogging time by 4 minutes each week. Write the general term of this arithmetic sequence, and find how many whole weeks it takes for him to reach a jogging time of one hour.

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. - $a _ { n } = a _ { n - 1 } - 6 , a _ { 1 } = 35$

Use Summation Notation - $\sum _ { i = 3 } ^ { 5 } \left( i ^ { 2 } - 8 \right)$

Use Factorial Notation - $a _ { n } = \frac { ( n + 1 ) ! } { n ^ { 4 } }$

Write a formula for the general term (the nth term) of the geometric sequence. - $- \frac { 1 } { 3 } , \frac { 1 } { 24 } , - \frac { 1 } { 192 } , \frac { 1 } { 1536 } , \ldots$

Write a formula for the general term (the nth term) of the geometric sequence. - $- 5 , - 10 , - 20 , - 40 , - 80 , \ldots$

Find the term indicated in the expansion. - $( 4 x + 3 ) ^ { 5 }$ ; 5 th term

Use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum. -A theater has 36 rows with 26 seats in the first row, 30 in the second row, 34 in the third row, and so forth. How many seats are in the theater?

Use Summation Notation - $\sum _ { i = 1 } ^ { 4 } \left( - \frac { 1 } { 4 } \right) ^ { i }$

Probability 1 Compute Empirical Probability -Measurements of the height of a group of men entering a particular college produced the following table. What is the probability that a man entering the college is 68-69 inches tall?

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: $\frac { 3 } { 3 } , \frac { 3 } { 6 } , \frac { 3 } { 12 } , \ldots$

Find the Value of an Annuity -To save for retirement, you decide to deposit $2250 into an IRA at the end of each year for the next 40 years. If the interest rate is 8% per year compounded annually, find the value of the IRA after 40 years.

Use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum. - $\sum _ { \mathrm { i } = 1 } ^ { 90 } - 4 \mathrm { i }$

Write Terms of a Geometric Sequence - $a _ { 1 } = 3 ; r = - 4$

Use the Permutations Formula -In how many ways can Susan arrange 10 books into 4 slots on her bookshelf?

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. -Carla takes a job with a starting salary of $26,000 for the first year with an annual increase of 6% beginning in the second year. What is Carla's salary, to the nearest dollar, in the seventh year?

Find the term indicated in the expansion. - $( 2 x + 5 ) ^ { 5 } ; 5$ th term

Use Factorial Notation - $a _ { n } = \frac { n ^ { 2 } } { ( n + 1 ) ! }$