Arithmetic or Geometric?
-5, -10, -15, -20
This is an Arithmetic sequence
Common difference = -5
The Common Difference of:
-20, -23, -26, -29...
Common difference = -3
What is r?
common ratio
Write an equation for the nth term (explicit) of the geometric sequences.
3, 15, 75, 375, 1875, ...
an = 3(5)n-1
On the first test, they score 65 points. Each test after, their score increases by 3 points.
What kind of sequence is represented in this problem?
Arithmetic
3, 12, 21, 30...
This is an Arithmetic Sequence?
Common difference = 9
The Common Ratio of:
3, -6, 12, -24, 48...
Common ratio = -2
What is a1 ?
What is an?
a1=the first term
an=the nth term
Write an equation for the nth term (explicit) of the arithmetic sequences.
3, 8, 13, 18, 23, ...
an = 3+5(n - 1)
Charlotte is starting a running plan. In the first week, she runs 5 miles. Instead of adding the same amount each week, her plan is to increase her mileage by 20% each week.
Write the explicit formula for the scenario.
an = 5 (1.20)n-1
-2, -4, -8, -16...
This is a Geometric Sequence?
Common ratio = 2
The Common Difference of:
18, 22, 26, 30...
Common difference = 4
When we see %, what sequence are looking for?
geometric
Write an equation for the nth term (explicit) of the geometric sequences.
1, -2, 4, -8, 16, ....
an=1(-2)n-1
In week 1, a person lifts 50 pounds. Each week, they increase the weight by 7 pounds. How much will they lift in week 14?
141 pounds
2, -6, 18, -54...
This is a Geometric Sequence?
Common ratio = -3
The Common Ratio of the Sequence:
3, 9, 27, 81...
Common ratio = 3
What kind of function is represented by an arithmetic sequence?
linear
Write an equation for the nth term (explicit) of the arithmetic sequences. Then find the 7th term.
-6, 1, 8, 15, 22, ...
an = -6+7(n-1)
a7 = 36
Maria is reading a book series. In the first week, she reads 20 pages. Each week, she reads 5 more pages than the previous week. How many pages will she read in the 10th week?
65 pages
-4, 2, -1, 1/2
This is a Geometric sequence
Common ratio: -1/2
The Common Ratio of:
1000, 200, 40, 8...
Common ratio = 1/5 or 0.2
Why use the explicit formula for word problems instead of the recursive formula?
Explicit formulas save time and allow us to solve directly for a term.
For recursive formulas, we need to know all the terms before it to find the next one.
Write a recursive and explicit equation for the geometric sequences. Solve for the 12th term.
128, 64, 32, 16, 8, ...
an=(1/2)*an-1 ; a1=128
an= 128(1/2)n-1
a12= 0.0625 OR (1/16)
A social media page is growing in popularity. In its first week, the page has 200 followers. Each week, the number of followers increases by 15%. If this pattern continues, how many followers will the page have in the 12th week? Round to the nearest follower.
931