Lesson 3.12 Applications of Arithmetic Sequences
description
Transcript of Lesson 3.12 Applications of Arithmetic Sequences
LESSON 3.12APPLICATIONS OF
ARITHMETIC SEQUENCES
HOW TO IDENTIFY AN ARITHMETIC SEQUENCE In a word problem, look for a constant
value being used between each term. This will indicate a common difference, d, and
an arithmetic sequence Example:
Determine whether each situation has a constant value between each term.
1. The height of a plant grows 2 inches each day.2. The cost of a video game increases by 10%
each month.3. Johnny receives 5 dollars each week for an
allowance.
STEPS TO CREATING AN EQUATION1. Create a visual representation of the
word problem using the template given.2. Identify the common difference, and
the first term, 3. Determine which formula would best fit
the situation (Recursive or Explicit)REMEMBER: Recursive formula helps us get
the next term given the previous term while explicit formula gives us a specific term.
4. Plug and in to the formula from step 2.5. Evaluate the formula for the given term.6. Interpret the result.
EXAMPLE 1 You visit the Grand Canyon and drop a
penny off the edge of a cliff. The distance the penny will fall is 16 feet the first second, 48 feet the next second, 80 feet the third second, and so on in an arithmetic sequence. What is the total distance the object will fall in 6 seconds?
Example 1:Title Sequence
DescriptionPicture
EXAMPLE 1 You visit the Grand Canyon and drop a
penny off the edge of a cliff. The distance the penny will fall is 16 feet the first second, 48 feet the next second, 80 feet the third second, and so on in an arithmetic sequence. What is the total distance the object will fall in 6 seconds?
1. Identify and The given sequence is 16, 48, 80, …
EXAMPLE 1 1. 2. Determine which formula would
best fit the situation. Since we want the distance after 6
seconds, we will use the explicit formula which is used to find a specific term.
Explicit Formula:
EXAMPLE 13. Plug and in to the formula from
step 2. If we plug in and from step 1, we get:
Simplify: Distribute Combine Like
Terms
EXAMPLE 13. 4. Evaluate the formula for the
given value. In the problem, we are looking for the
total distance after 6 seconds. Therefore, we will plug in 6 to the equation from step 3.
EXAMPLE 14. 5. Interpret the result
The problem referred to the total distance in feet, therefore:
After 6 seconds, the penny will have fallen a total distance of 176 feet.
EXAMPLE 2 Tom just bought a new cactus plant for
his office. The cactus is currently 3 inches tall and will grow 2 inches every month. How tall will the cactus be after 14 months?
1. Identify and
Difference between months
Height after 1 month
Example 2:Title Sequence
DescriptionPicture
EXAMPLE 2 1. 2. Determine which formula would
best fit the situation. Since we want the distance after 14
months, we will use the explicit formula which is used to find a specific term.
Explicit Formula:
EXAMPLE 23. Plug and in to the formula from
step 2. If we plug in and from step 1, we get:
Simplify: Distribute Combine Like
Terms
EXAMPLE 23. 4. Evaluate the formula for the
given value. In the problem, we are looking for the
height after 14 months. Therefore, we will plug in 14 to the equation from step 3.
EXAMPLE 24. 5. Interpret the resultThe problem referred to the height in
inches, therefore:After 14 months, the cactus will be 31
inches tall.
EXAMPLE 3 Kayla starts with $25 in her allowance
account. Each week that she does her chores, she receives $10 from her parents. Assuming she doesn’t spend any money, how much money will Kayla have saved after 1 year?
1. Identify and
Difference between weeks
Amount after 1 week
Example 3:Title Sequence
DescriptionPicture
EXAMPLE 3 1. 2. Determine which formula would
best fit the situation. Since we want the distance after 1
year (Which is ___ weeks), we will use the explicit formula which is used to find a specific term.
Explicit Formula:
EXAMPLE 33. Plug and in to the formula from
step 2. If we plug in and from step 1, we get:
Simplify: Distribute Combine Like
Terms
EXAMPLE 33. 4. Evaluate the formula for the
given value. In the problem, we are looking for the
amount after 52 weeks. Therefore, we will plug in 52 to the equation from step 3.
EXAMPLE 34.
5. Interpret the resultThe problem referred to the amount of
money, therefore:After 52 weeks, Kayla will have saved
$545.
YOU TRY! The sum of the interior angles of a
triangle is 180º, of a quadrilateral is 360º and of a pentagon is 540º. Assuming this pattern continues, find the sum of the interior angles of a dodecagon (12 sides).
You Try!Title Sequence
DescriptionPicture
YOU TRY!
Formula:
Plug in 12
Interpret: