Exam 11: Sequences, Induction, and Probability

Find the Probability of One Event and a Second Event Occurring -Two 6-sided dice are rolled. What is the probability that the sum is odd and the number on one of the dice is a 3 ?

Additional Concepts - $\frac{5 C_{3} \cdot 4^{C}}{16 C_{13}}$

Express the repeating decimal as a fraction in lowest terms. - $0 . \overline { 468 }$

Use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum. -A new exhibit is scheduled to open at the local museum. Museum officials expect that 9000 people will visit the exhibit in its first week, and that the number of visitors will drop by 40 people per week after the first week during the first 6 months. Find the total number of visitors expected in the exhibit's first 7 weeks.

Write the first four terms of the sequence whose general term is given. - $\mathrm { a } _ { \mathrm { n } } = ( - 2 ) ^ { \mathrm { n } }$

Use the Fundamental Counting Principle -Lisa has 4 skirts, 6 blouses, and 3 jackets. How many 3-piece outfits can she put together assuming any piece goes with any other?

Geometric Sequences and Series 1 Find the Common Ratio of a Geometric Sequence - $2,8,32,128,512$

Use Recursion Formulas - $a _ { 1 } = - 4$ and $a _ { n } = a _ { n - 1 } - 1$ for $n \geq 2$

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

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

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. - $a _ { n } = 5 n ^ { 2 }$

Write the first four terms of the sequence whose general term is given. - $a _ { n } = ( - 1 ) ^ { n + 1 } ( n + 8 )$

Write a formula for the general term (the nth term) of the geometric sequence. - $0.00009,0.0009,0.009,0.09 , \ldots$

Express the sum using summation notation. Use a lower limit of summation not necessarily 1 and k for the index of summation. - $5 + 6 + 7 + 8 + \ldots + 22$

Find the Probability of One Event and a Second Event Occurring -If two 12 -sided dice are rolled what is the probability that both numbers will be even?

Use the Formula for the Sum of the First n Terms of an Arithmetic Sequence -Find the sum of the first 30 terms of the arithmetic sequence: 7, 3, -1, -5, . . .

Use the Fundamental Counting Principle -A student must choose 1 of 5 science electives, 1 of 8 social studies electives, and 1 of 7 language electives. How many possible course selections are there?

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. - $3 + \frac { 3 } { 4 } + \frac { 3 } { 16 } + \ldots + \frac { 3 } { 4 ^ { n - 1 } } = 4 \left( 1 - \frac { 1 } { 4 ^ { n } } \right)$

Use the Fundamental Counting Principle -A restaurant offers a choice of 5 salads, 10 main courses, and 2 desserts. How many possible 3-course meals are there?

Find a Particular Term in a Binomial Expansion - $( x + 6 ) ^ { 20 }$