Question

1 multiple choice 4 points
what is the fifth term of the arithmetic sequence 8, 6, 4, ...?
4
0
-2
16
8
2 multiple choice 4 points
the average of a set of five integers is 16. when a sixth number is included in the set, the average of the set increases to 18. what is the sixth number?
21
24
20
18
28
3 multiple choice 4 points
there are 16 ounces in a pound. if 1.5 pounds of hamburger costs $2.88, what is the cost per ounce?
$1.92
$0.09
$0.18
$0.12
$4.32

Explanation:

Step1: Identify arithmetic sequence parameters

Given arithmetic sequence: $a_1=8$, common difference $d=6-8=-2$. The nth term formula is $a_n=a_1+(n-1)d$.

Step2: Calculate 5th term of sequence

Substitute $n=5$, $a_1=8$, $d=-2$:
$a_5=8+(5-1)\times(-2)=8-8=0$

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Step1: Find sum of 5 integers

Sum = average $\times$ count: $S_5=16\times5=80$

Step2: Find sum of 6 integers

New average = 18, so $S_6=18\times6=108$

Step3: Calculate 6th number

6th number = $S_6-S_5=108-80=28$

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Step1: Convert pounds to ounces

1.5 pounds = $1.5\times16=24$ ounces

Step2: Calculate cost per ounce

Cost per ounce = $\frac{\text{Total Cost}}{\text{Total Ounces}}=\frac{2.88}{24}=0.12$

Answer:

1. 0
2. 28
3. $0.12$