An electrician earns $110 after his first hour of working for a client. His total pay based on the number of hours worked can be represented using the sequence shown.
110, 130, 150, 170, ...
Which recursive formula can be used to determine the total amount of money earned for each successive hour worked based on the amount of money currently earned?
f(n + 1) = f(n) + 20
f(n + 1) = f(n) + 110
f(n + 1) = f(n + 1) + 20
f(n + 1) = f(n + 1) + 110
Answers
Answered by
18
Let our function of payment be f(x)
Here x = no. of hours worked
Our sequence is:
110, 130, 150, 170
So, f(1) = 110
f(2) = 130
f(3) = 150
f(4) = 170
f(2) - f(1) = 20
or f(x + 1) - f(x) = 20
The payment is linked to hours times 20 so, it means that every hour he works, he gets 20 dollars.
Therefore, our function is
f(n + 1) = f(n) + 20 as for every successive hour, he gets 20$.
Here x = no. of hours worked
Our sequence is:
110, 130, 150, 170
So, f(1) = 110
f(2) = 130
f(3) = 150
f(4) = 170
f(2) - f(1) = 20
or f(x + 1) - f(x) = 20
The payment is linked to hours times 20 so, it means that every hour he works, he gets 20 dollars.
Therefore, our function is
f(n + 1) = f(n) + 20 as for every successive hour, he gets 20$.
Answered by
7
The sequence
110, 130, 150...............is an AP with common difference 20.
Now, nth term of this sequence is
f(n) = a +(n-1)d
f(n) = 110 + (n-1)20
f(n) = 110 + 20n - 20........(1)
Replace n by n+1
f(n+1) = 110 + 20n.........(2)
(2) - (1) gives
f(n+1) - f(n) = 20
f(n+1) = f(n) + 20 which is the required recursive formula
I hope this answer helps you
110, 130, 150...............is an AP with common difference 20.
Now, nth term of this sequence is
f(n) = a +(n-1)d
f(n) = 110 + (n-1)20
f(n) = 110 + 20n - 20........(1)
Replace n by n+1
f(n+1) = 110 + 20n.........(2)
(2) - (1) gives
f(n+1) - f(n) = 20
f(n+1) = f(n) + 20 which is the required recursive formula
I hope this answer helps you
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