Question

quiz 8 (1.8 to 1.10) name:
algebra 2
1 determine if the given sequence is arithmetic or geometric.
a. 1/3, 1, 3, 9, 27
b. 1/4, 1/2, 3/4, 1

1. a sequence starts with 5. state the next three terms given the rules below.

a. each term is 4 more than the previous term.
5, _, _, _
b. each term is triple the previous.
5, _, _, _

1. a city bus charges $0.50 per ride if you buy a discount card for $10 up - front. let b be the total cost, in dollars, of taking rides on the bus. complete the table for function b, write the recursive and explicit rules then sketch the graph of the function.

n	b(n)
0	10
1	10.50

|2|
|3|
|4|
recursive rule:
explicit rule:

Explanation:

Step1: Determine sequence type for 1.a

Check the ratio between consecutive terms. $\frac{1}{\frac{1}{3}} = 3$, $\frac{3}{1}=3$, $\frac{9}{3}=3$, $\frac{27}{9}=3$. Since there is a common - ratio of 3, it is geometric.

Step2: Determine sequence type for 1.b

Check the difference between consecutive terms. $\frac{1}{2}-\frac{1}{4}=\frac{1}{4}$, $\frac{3}{4}-\frac{1}{2}=\frac{1}{4}$, $1 - \frac{3}{4}=\frac{1}{4}$. Since there is a common difference of $\frac{1}{4}$, it is arithmetic.

Step3: Find next terms for 2.a

The first term is 5. Since each term is 4 more than the previous term, the next terms are $5 + 4=9$, $9+4 = 13$, $13 + 4=17$.

Step4: Find next terms for 2.b

The first term is 5. Since each term is triple the previous term, the next terms are $5\times3 = 15$, $15\times3=45$, $45\times3 = 135$.

Step5: Complete the table for 3

For $n = 2$, $B(2)=10+0.5\times2=11$. For $n = 3$, $B(3)=10+0.5\times3 = 11.5$. For $n = 4$, $B(4)=10+0.5\times4=12$.

Step6: Write recursive rule for 3

$B(0)=10$, $B(n)=B(n - 1)+0.5$ for $n\geq1$.

Step7: Write explicit rule for 3

$B(n)=10 + 0.5n$.

Answer:

1.a. Geometric
1.b. Arithmetic
2.a. 9, 13, 17
2.b. 15, 45, 135
3.

n	B(n)
1	10.50
2	11
3	11.5
4	12

Recursive Rule: $B(0)=10$, $B(n)=B(n - 1)+0.5$ for $n\geq1$
Explicit Rule: $B(n)=10 + 0.5n$