Question

3 Performance Assessment Form B

Alani receives a collection of coins from her mother as a gift.
She wants to start collecting coins. She projects the total
number of coins she believes she will own over the next 5 years
and graphs the results.
1. The graph shows the relationship between the number of
coins Alani believes she will own and the amount of time
she thinks it will take to acquire them.
Explicitan= a₁ (n-1) d
an=20 (n-1)15
an=5+15n
Ö
Part A
Complete the table using the data from the graph. What
type of sequence do the data represent? What is a recursive
formula that represents the total number of coins for the nth
year if Alani keeps collecting coins at the same rate? What is
an explicit formula that represents the situation? Explain.
recursive an=an-i+d
explanation:
an=an-1*15, a₁ = 20
80
4
Year
12 3 4 5
Actual Number of Coins 18 29 36 59 62
60
40
z 20
0
0
2023
Oguliat
sawasrealize.com
6
A recursive formula which
represents the total amount
coins for the nth formula
is an=an-1+ 15 and an
explicit formula which represents
the situation is an=Stisn.
Year
2
3
4
5
•
2 4
Year
•
Number
of Coins
20
35
50
65
80
Part B
From Part A, how is the explicit formula of the sequence related to a linear
function? What is the linear function for the number of coins f(x) as it relates
to the number of years x? What is the domain of f(x)?
2. The data in the table below shows the actual total number of coins Alani owns
over a five-year period.

Answer 1

Part A:

The data in the table represents an arithmetic sequence, as the number of coins Alani will own increases by a constant amount each year. The recursive formula for this sequence is an=an-1 + 15, where a1 = 20, and the explicit formula is an = 20 + 15n.

Part B:

The explicit formula of the sequence is related to a linear function as it is of the form y = mx + b, where m is the common difference (15) and b is the first term (20). The linear function for the number of coins f(x) as it relates to the number of years x is f(x) = 15x + 20. The domain of f(x) is all real numbers, as there are no restrictions on the number of years x that Alani can collect coins.

Explanation: