Arithmetic or Geometric?
find d or r
find d or r
-5, -10, -15, -20
Arithmetic
Common difference = -5
Write a recursive rule given the first term is 2 and the common ratio is 3
f(1) = 2, f(n) = 3 f(n - 1)
Write an explicit rule given the first term is 2 and the common ratio is 3
f(n) = 2(3)n-1
Write an equation for the nth term (explicit) of the geometric sequences. And find f(10)
3, 15, 75, 375, 1875, ...
f(n) = 3*5n-1
f(10) = 5,859,375Joanne and her friends went on a hiking vacation in a national park. They hiked 3 miles their first day. They went on a 6 mile hike and a 12 mile hike on days 2 and 3. If they continue to increase their distance in a geometric sequence, how many miles will they hike on day 4?
24 miles
375, 75, 15, 3, 3/5 ...
Geometric
Common Ratio = 0.2
Write a recursive rule for
-4, 2, -1, -1/2
f(1) = -4, f(n) = (-0.5) f(n - 1)
What are the first 3 terms and the common ratio of f(n) = 5 (3)n - 1
5, 15, 45 and r = 3
Write an equation for the nth term (explicit) of the geometric sequences. Then find f(8) round to nearest hundredth
324, 108, 36, 12, 4, ...
f(n) = 324 * (1/3)n-1
f(8) = 0.15
A manufacturing plant produces 112 widgets on their first day. Each day they triple their production. What are the first 4 terms of the geometric sequence and what is the common ratio?
112, 336, 1008, 3024 and r = 3
-2, -4, -8, -16...
Geometric
Common ratio = 2
What are the first three terms of the recursive rule? And what is the common ratio?
f(1) = 5, f(n) = -2 f(n - 1)
5. -10, 20, and r = -2
Write the explicit equation for the following geometric sequence:
1.5, -6, 24
f(n) = 1.5(-4)n-1
Write the explicit rule for the geometric sequence that has the following points. Then find the 7th term
(1, 1) and (2, -2)
f(n)=1 * (-2)n-1
f(7) = 64
You buy a computer for $6500 and it depreciates 14% per year. What is the value of the computer after 3 years?
$4134.36
2, -6, 18, -54...
Geometric
Common ratio = -3
Write the recursive rule for the geometric sequence that has the points
(1, 2), (2, -6), (3, 18), (4, -54)
f(1) = 2, f(n) = -3 f(n - 1)
Write the explicit rule for the geometric sequence that has the points
(1, 2), (2, -6), (3, 18), (4, 54)
f(n) = 2(-3)n - 1
Write an equation for the nth term (explicit) of the geometric sequences. Then find the 8th term
(1, 3) and (2, 6)
f(n)= 3*(2)n-1
f(8)= 384
In 2022 you bought a baseball card for $50. If it increases in value 4.6% per year, how much is it worth in 2037?
$98.16
-4, 2, -1, 1/2
Geometric
Common ratio: -1/2
Write a recursive and explicit equation for the geometric sequences.
128, 64, 32, 16, 8, ...
f(n)=(1/2)*f(n-1) ; f(1)=128
f(n)= 128*(1/2)n-1
Write the explicit rule for the geometric sequence that has the points
(1, 5), (2, 2.5), (3, 1.25), (4, 0.625)
f(n) = 5 (0.5)n - 1
Write the explicit rule for the geometric sequence that has the following points. Then find the 7th term
(1, 375), (2, 75), (3, 15) (4, 3)
f(n) = 375 (0.2)n - 1
f(7) = 0.024
Alice is conducting an experiment with a radioactive element that has a 1/2 life of one day. After the first day she has 500g. How much will she have after 6 days?
15.625 g