Exam 11: Sequences, Induction, and Probability

Find the indicated sum. Use the formula for the sum of the first n terms of a geometric sequence. - $\sum _ { \mathrm { i } = 1 } ^ { 5 } \frac { 4 } { 3 } \cdot 2 ^ { \mathrm { i } }$

Expand a Binomial Raised to a Power - $\left( x ^ { 2 } - 3 y \right) ^ { 4 }$

Expand a Binomial Raised to a Power - $( 2 x - 2 ) ^ { 4 }$

Write Terms of an Arithmetic Sequence - $\mathrm { a } _ { \mathrm { n } } = \mathrm { a } _ { \mathrm { n } } - 1 - 8 ; \mathrm { a } _ { 1 } = - 11$

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 $a _ { 60 }$ when $a _ { 1 } = 17 , d = - 3$ .

Evaluate the given binomial coefficient. - $\left( \begin{array} { l } 9 \\ 3 \end{array} \right)$

Use the Formula for the Sum of the First n Terms of an Arithmetic Sequence - $\sum_{i=1}^{13}(4 i-4)$

Write a formula for the general term (the nth term) of the geometric sequence. - $2 , - 4,8 , - 16,32 , \ldots$

Find the Probability of One Event and a Second Event Occurring -A card is drawn from a well-shuffled deck of 52 cards. What is the probability of getting a red 4 ?

Use the Fundamental Counting Principle -There are 5 roads leading from Bluffton to Hardeeville, 9 roads leading from Hardeeville to Savannah, and 5 roads leading from Savannah to Macon. How many ways are there to get from Bluffton to Macon?

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

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 pendulum bob swings through an arc 70 inches long on its first swing. Each swing thereafter, it swings only 80% as far as on the previous swing. What is the length of the arc after 8 swings? Round to two decimal places.

Use Factorial Notation - $\frac { 8 ! } { 7 ! }$

Express the sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation. - $3 + 6 + 9 + \ldots + 27$

Use the Combinations Formula -Ron finds 8 books at a bookstore that he would like to buy, but he can afford only 5 of them. In how many ways can he make his selection? How many ways can he make his selection if he decides that one of the books is a must?

Use the Formula for the Sum of the First n Terms of an Arithmetic Sequence -Find 2 + 4 + 6 + 8 + . . ., the sum of the first 45 positive even integers.

Use the Formula for the Sum of the First n Terms of a Geometric Sequence -Find the sum of the first 14 terms of the geometric sequence: $\frac { 1 } { 4 } , - \frac { 3 } { 4 } , \frac { 9 } { 4 } , - \frac { 27 } { 4 } , \frac { 81 } { 4 } , \ldots$

Use the Combinations Formula -From 9 names on a ballot, a committee of 4 will be elected to attend a political national convention. How many different committees are possible?

Expand a Binomial Raised to a Power - $( x + 3 y ) ^ { 6 }$

Additional Concepts - $1 - \frac { { } _ { 9 } \mathrm { P } _ { 6 } } { { } _ { 12 } \mathrm { P } _ { 9 } }$