Exam 7: Arithmetic Sequence: Common Difference and First n Terms

Find the first term and the common ratio for the geometric sequence. Round approximations to the nearest hundredth. - $a _ { 2 } = 18 , a _ { 4 } = 2$

Find the first term and the common ratio for the geometric sequence. Round approximations to the nearest hundredth. - $a _ { 2 } = 6.3 , a _ { 5 } = 58.34$

Identify the equation as a parabola, circle, ellipse, or hyperbola. - $x ^ { 2 } + y ^ { 2 } = 36$

Find the probability. -Two 6-sided dice are rolled. What is the probability the sum of the two numbers on the die will be 5?

Provide an appropriate response. -The sum of an infinite geometric series exists if:

100 employees of a company are asked how they get to work and whether they work full time or part time. The figure below shows the results. If one of the 100 employees is randomly selected, find the probability that the Person does not commute by public transportation. 1. Public transportation: 8 full time, 8 part time 2. Bicycle: 5 full time, 3 part time 3. Drive alone: 28 full time, 33 part time 4. Car pool: 9 full time, 6 part time

Write the first n terms of the given arithmetic sequence (the value of n is indicated in the question). -The first term is 20, and the common difference is 7; $n = 5$

How many ways can a president, vice-president, secretary, and treasurer be chosen from a club with 10 members? Assume that no member can hold more than one office.

Discuss the graph of the equation $\frac { x ^ { 2 } } { a ^ { 2 } } + \frac { y ^ { 2 } } { b ^ { 2 } } = 1 \text { if } a = b$

Decide whether the given sequence is finite or infinite. - $a _ { 1 } = 7 ; \text { for } n \geq 2 , a _ { n } = 3 \cdot a _ { n - 1 } + 3$

Write an equation for the ellipse. - $e = \frac { 7 } { 25 } ; \text { foci at } ( 7,0 ) , ( - 7,0 )$

Write an equation for the hyperbola. - $x$ -intercepts $( \pm 9,0 )$ , foci at $( - \sqrt { 117 } , 0 ) , ( \sqrt { 117 } , 0 )$

Find the nth term of the geometric sequence. - $a _ { 1 } = 5 , r = 5 , n = 6$

A man earned $3000 the first year he worked. If he received a raise of $600 at the end of each year, what was his salary during the 15th year?

Use the summation properties to evaluate the series. The following rules may be needed: $\sum _ { i = 1 } ^ { n } i = \frac { n ( n + 1 ) } { 2 } ; \quad \sum _ { i = 1 } ^ { n } i ^ { 2 } = \frac { n ( n + 1 ) ( 2 n + 1 ) } { 6 } ; \quad \sum _ { i = 1 } ^ { n } i ^ { 3 } = \frac { n ^ { 2 } ( n + 1 ) ^ { 2 } } { 4 }$ - $\sum _ { i = 1 } ^ { 5 } \left( 3 + 2 i ^ { 3 } \right)$

Find the eccentricity of the conic section shown in the graph. - $x = - \frac { 1 } { 2 }$

Give the focus, directrix, and axis for the parabola. - $x = 9 y ^ { 2 }$

It can be shown that $( 1 + x ) ^ { n } = 1 + n x + \frac { n ( n - 1 ) } { 2 ! } x ^ { 2 } + \frac { n ( n - 1 ) ( n - 2 ) } { 3 ! } x ^ { 3 } \ldots$ is true for any real number $n$ (not just positive integer values) and any real number $x$ , where $| x | < 1$ . Use this series to approximate the given number to the nearest thousandth. - $1.06 ^ { 3 }$

Suppose that certain bacteria can double their size and divide every 30 minutes. Write a recursive sequence that describes this growth where each value of $\mathrm { n }$ represents a 30 -minute interval. Let $\mathrm { a } _ { 1 } = 451$ represent the initial number of bacteria present.

List the elements in the sample space of the experiment. -A box contains 10 red cards numbered 1 through 10. List the sample space of picking one card from the box.