How do you write a recursive formula
1 answer:
You need to show how a term of formula is based on a previous term.
For example, let's say you have the sequence 3, 6, 9, 12, ...
(multiples of 3).
As a regular function, you can have y = 3x, for the domain of all integers greater than 0. Since the domain is 1, 2, 3, 4, ..., when you multiply those numbers by 3, to get y, you generate the sequence.
To define the sequence recursively, you must base each new number on the previous number.
Start by stating the first term.
a1 = 3
If you look at the sequence, 3, 6, 9, ..., you see it has a constant difference, and it is an arithmetic sequence, so to generate a term, you need to add 3 to the previous term.
Once we defined the first term to be 3, the next term is a2 = 3 + 3 = 6
Then a3 = 6 + 3 = 9, etc.
To define the sequence recursively, just generalize the addition of 3 to a term to get the next term.
For example, let's say you have the sequence 3, 6, 9, 12, ...
(multiples of 3).
As a regular function, you can have y = 3x, for the domain of all integers greater than 0. Since the domain is 1, 2, 3, 4, ..., when you multiply those numbers by 3, to get y, you generate the sequence.
To define the sequence recursively, you must base each new number on the previous number.
Start by stating the first term.
a1 = 3
If you look at the sequence, 3, 6, 9, ..., you see it has a constant difference, and it is an arithmetic sequence, so to generate a term, you need to add 3 to the previous term.
Once we defined the first term to be 3, the next term is a2 = 3 + 3 = 6
Then a3 = 6 + 3 = 9, etc.
To define the sequence recursively, just generalize the addition of 3 to a term to get the next term.
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Following are the general entry to the given question:
For Question 1:
Date Account Titles and Explanation Dr Cr
31-Jan-2024 Revenue Service $17,500
Summary of Income $17,500
(Finishing the revenue account)
31-Jan-2024 Summary of Income $7,100
Expense of Salary $3,600
Expense on rent $1,800
Expense of Depreciation - equipment $300
Expense on Supplies $400
Expense on Utilities $1,000
(To close the expenditure account)
31-Jan-2024 Summary of Income $10,400
Retained Earnings $10,400
(To bring net income into line with retained profits)
31-Jan-2024 Retained Earnings $1,000
Dividend $1,000
(To close net dividend to retained earnings)
For Question 2:
A net income of $10,400 is generated. They may compute it by subtracting total expenses from the entire revenue.
Total Revenue= $17,500
Total Expenses=$7,100
- Please find the complete question in the attachment file.
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