Geometric Sequences
What are the next three terms of the sequence 6, 18, 54, ... ?
162, 486, 1458
Express in radical form: 2^(1/2)
√2
√25
5
Solve:
5^(x-1) = 5^4
x = 5
Name the parent function:
y = 5 * 2^(x+2) - 6
y = 2^x
Write an explicit formula for the sequence 5, 10, 20, 40, ...
g_n = 5 * (2)^(n-1)
Express using Rational Powers:
(A) 3√(4)^5
(B) 5√(3)^4
(A) 4^(5/3)
(B) 3^(4/5)
Create a factor tree for the value 100.
Answers vary, 100 = 2^2 * 5^2
Solve:
2^(3x) = 4
x = (2/3)
Name the transformation:
y = 2^x + 10
Translate Up 10 Units
Is the following sequence geometric? Justify your answer.
60, 36, 21.6, 12.96, ...
Yes, there is a common ratio (multiplyer) of 0.6)
Express using a rational power in simplest form:
4√(7)^8
7^2 or 49
Simplify √32
4√2
Solve:
3^(2x + 1) = 27
x = 1
Name every transformation:
y = - 2^(x - 3) + 1
- Reflection over x-axis (flip)
- Translate Right 3 Units
- Translate Up 1 Unit
Rewrite the explicit geometric formula in function form:
g_n = 4 * (1/2)^(n-1)
y = 8(1/2)^x
Simplify and then rewrite in radical form:
2^(1/3) * 2^(1/3)
2^(2/3) = √(2)^3
Simplify √700
10√7
Solve:
2^(5x) = 1024
x = 2
Identify each transformation, the domain and range, and name the asymptote of the graph:
y = - 3^(x+1) - 2
- Reflection over x-axis (flip)
- Translate Left 1 Unit
- Translate Down 2 Units
Domain : All real numbers
Range: y < -2
Asymptote: y = -2
Write a function that contains the points (0,3) (1,6) and (2, 12).
g_n = 3 * 2^x
Express in radical form, then simplify your answer.
4^(3/2)
√(4)^3 = √64 = 8
Simplify √(768x^2)
16x√3
5^(3x - 6) = 3125
x = (11/3)
Sketch an accurate graph of y = 2^x - 4 along with its parent function. Label the asymptotes. Identify the domain and range.
Good luck bro