Question

multiple choice: write the letter of the correct choice in the blank. show all work.
b 1. for the arithmetic sequence 90, 87, 84, 81, ..., what would the 31st term be?
a. -3
b. 0
c. 177
d. 180
e. none of these
(work shown: 87 - 90 = -3; 90 + (31 - 1)(-3); 90 + (30)(-3); 90 - 90 = 0)
2. for an arithmetic sequence that starts with -2 and has a common difference of 2, what would the 15th term be?
a. -32
b. -30
c. 26
d. 28
e. none of these

short answer: write the answer in the blank. show all work.
3. write the equation of a line with a slope of -1 and a y-intercept of (0, 2).
4. write the equation of the line graphed below.
(image of a coordinate plane with a line)
5. express the equation 2x - 3y = 6 in slope-intercept form.
6. for the arithmetic sequence -7, -17, -27, -37, -47, ..., what is the common difference?
quiz 11 cont.

Explanation:

Question 1

Step1: Recall arithmetic sequence formula

The formula for the \(n\)-th term of an arithmetic sequence is \(a_n = a_1+(n - 1)d\), where \(a_1\) is the first term, \(d\) is the common difference, and \(n\) is the term number.
Here, \(a_1 = 90\), \(d=87 - 90=- 3\), and \(n = 31\).

Step2: Substitute values into formula

Substitute \(a_1 = 90\), \(d=-3\), and \(n = 31\) into the formula:
\(a_{31}=90+(31 - 1)\times(-3)\)
\(=90 + 30\times(-3)\)
\(=90-90\)
\(=0\)

Step1: Recall arithmetic sequence formula

The formula for the \(n\)-th term of an arithmetic sequence is \(a_n=a_1+(n - 1)d\), where \(a_1=-2\), \(d = 2\), and \(n = 15\).

Step2: Substitute values into formula

Substitute \(a_1=-2\), \(d = 2\), and \(n = 15\) into the formula:
\(a_{15}=-2+(15 - 1)\times2\)
\(=-2+14\times2\)
\(=-2 + 28\)
\(=26\)

Step1: Recall slope - intercept form

The slope - intercept form of a line is \(y=mx + b\), where \(m\) is the slope and \(b\) is the \(y\)-intercept.
Here, \(m=-1\) and \(b = 2\) (since the \(y\)-intercept is \((0,2)\)).

Step2: Write the equation

Substitute \(m=-1\) and \(b = 2\) into the slope - intercept form: \(y=-x + 2\)

Answer:

b. 0

Question 2