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. - $- 3,3,9,15,21 , \ldots$

Find the Probability of One Event or a Second Event Occurring -A lottery game has balls numbered 1 through 15 . What is the probability of selecting an even numbered ball or a 13?

Find the term indicated in the expansion. - $( x + 2 y ) ^ { 12 }$ ; 11th term

Use the Formula for the Sum of the First n Terms of an Arithmetic Sequence -Find the sum of the first 42 terms of the arithmetic sequence: 2, 4, 6, 8, . . .

Use the Formula for the Sum of the First n Terms of an Arithmetic Sequence - $\sum _ { i = 1 } ^ { 60 } - 5 i$

Find the Probability of One Event or a Second Event Occurring -A card is drawn from a deck of 52 cards. What is the probability that it is a picture card (Jack, Queen, King) or a heart?

Use Factorial Notation - $\frac { n ( n + 5 ) ! } { ( n + 6 ) ! }$

Find the Value of an Annuity -Domenica invests $200 each quarter in a fixed-interest mutual fund paying annual interest of 6% compounded quarterly. How much will her account have in it at the end of 14 years?

Use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum. -A person puts $29 into a bank account on January 1, $39 on February 1, $49 on March 1, and so forth. How much has the person put into the bank account by December 30?

Evaluate the given binomial coefficient. - $\left( \begin{array} { l } 8 \\ 4 \end{array} \right)$

Use the Combinations Formula -In a student government election, 6 seniors, 2 juniors, and 3 sophomores are running for election. Students elect four at-large senators. In how many ways can this be done?

Use Summation Notation - $\sum _ { i = 3 } ^ { 6 } \frac { i ! } { ( i - 1 ) ! }$

Write Terms of an Arithmetic Sequence - $a _ { n } = a _ { n } - 1 - 2.2 ; a _ { 1 } = - 14$

Write the first four terms of the sequence whose general term is given. - $a _ { n } = \frac { n + 1 } { 2 n - 1 }$

Write Terms of a Geometric Sequence - $a _ { n } = 3 a _ { n - 1 } ; a _ { 1 } = - 2$

Express the repeating decimal as a fraction in lowest terms. -A pendulum bob swings through an arc 80 inches long on its first swing. Each swing thereafter, it swings only 70% as far as on the previous swing. How far will it swing altogether before coming to a complete stop? Round to the nearest inch when necessary.

Find the Probability of One Event and a Second Event Occurring -A game spinner has regions that are numbered 1 through 9 . If the spinner is used twice, what is the probability that the first number is a 3 and the second is a 7 ?

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. - $\mathrm { a } _ { 1 } = 8 , \mathrm {~d} = 0.6$

Expand a Binomial Raised to a Power - $( x - 5 y ) ^ { 5 }$

Use the Formula for the Sum of an Infinite Geometric Series - $- 10 - 5 - \frac { 5 } { 2 } - \frac { 5 } { 4 } - \ldots$