The sequence is: 2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35, 38, 41, 44,...
How to Write this Sequence Recursively
Use this formula: an=an-1+r
First find the common difference,r, between the terms. In this case the common difference is 3 because each term is exactly three more than its previous term.
How to Write this Sequence Recursively
Use this formula: an=an-1+r
First find the common difference,r, between the terms. In this case the common difference is 3 because each term is exactly three more than its previous term.
Then substitute r for the common difference 3 resulting in this recursive formula...
a1=2 an = an-1+3
How to Write this Sequence Explicitly
Use this formula...
an=(First Term) + Common Difference(n-1)
In this case we have already found the common difference, 3.
Looking back at the sequence we find that the first term is 2.
Therefore, the formula would be...
an = 2 + 3(n-1)
a1=2 an = an-1+3
How to Write this Sequence Explicitly
Use this formula...
an=(First Term) + Common Difference(n-1)
In this case we have already found the common difference, 3.
Looking back at the sequence we find that the first term is 2.
Therefore, the formula would be...
an = 2 + 3(n-1)
Subtraction
A scientist is growing mold colonies in a lab. She starts with 1 mold. Every hour the amount of mold doubles. However, later she finds that some of the mold died equal to the number of hours the mold was growing. Write the function and find how much mold she had after 4 hours.
Function : f(x) = 2^x-x
Solution : She had 12 mold after 4 hours.
Multiplication
A worker is being payed 10 dollars for every hour he works. Write the function and find how much money he had after working 12 hours.
Function : f(x) = 10x
Solution : He earned 120 dollars after working 12 hours.
Addition
John had 3 cookies on his plate. He gets one for every minute he reads his book. Write the function and find how many cookies he has after 14 minutes of reading.
Function: f(x) = 3 + x
Solution: He had 17 cookies on his plate after reading 14 minutes.
Division
Bob has 64 cookies. He eats half of the number cookies he has each day. How many cookies did he have after 3 days?
Function: f(x) = 64/2^x
Solution: He had 8 cookies after three days.
Vertical Translations
Vertical translations are translations in which a function or graph is moved up or down. Performing a vertical translation would result in modifying the y-intercept of a function. However, performing a vertical translation will not modify the function's slope.
Original Function (red) : f(x) = 4x + 1
Translation 1(blue) : f(x) = 4x + 3
This translation's graph is located two units above the original function's graph.
Translation 2 (green) : f(x) = 4x + 5
This translation's graph is located four units above the original function's graph.
Translation 3 (purple) : f(x) = 4x -1
This translation's graph is located two units below the original function's graph.
A scientist is growing mold colonies in a lab. She starts with 1 mold. Every hour the amount of mold doubles. However, later she finds that some of the mold died equal to the number of hours the mold was growing. Write the function and find how much mold she had after 4 hours.
Function : f(x) = 2^x-x
Solution : She had 12 mold after 4 hours.
Multiplication
A worker is being payed 10 dollars for every hour he works. Write the function and find how much money he had after working 12 hours.
Function : f(x) = 10x
Solution : He earned 120 dollars after working 12 hours.
Addition
John had 3 cookies on his plate. He gets one for every minute he reads his book. Write the function and find how many cookies he has after 14 minutes of reading.
Function: f(x) = 3 + x
Solution: He had 17 cookies on his plate after reading 14 minutes.
Division
Bob has 64 cookies. He eats half of the number cookies he has each day. How many cookies did he have after 3 days?
Function: f(x) = 64/2^x
Solution: He had 8 cookies after three days.
Vertical Translations
Vertical translations are translations in which a function or graph is moved up or down. Performing a vertical translation would result in modifying the y-intercept of a function. However, performing a vertical translation will not modify the function's slope.
Original Function (red) : f(x) = 4x + 1
Translation 1(blue) : f(x) = 4x + 3
This translation's graph is located two units above the original function's graph.
Translation 2 (green) : f(x) = 4x + 5
This translation's graph is located four units above the original function's graph.
Translation 3 (purple) : f(x) = 4x -1
This translation's graph is located two units below the original function's graph.