The values in the table represent an exponential function. What is the common ratio of the associated geometric sequence?
Answers
Answer:
Step-by-step explanation:
The common ratio of the associated geometric sequence
The common ratio of the associated geometric sequence is 4
Given:
Table of exponential function
x y
1 9
2 36
3 144
4 576
5 2304
To Find:
Common Ratio of the associated geometric sequence
Solution:
Geometric sequence
A sequence of numbers in which the ratio between consecutive terms is constant and called the common ratio.
a , ar , ar² , ... , arⁿ⁻¹
The nth term of a geometric sequence with the first term a and the common ratio r is given by: aₙ = arⁿ⁻¹
Sum is given by Sₙ = a(rⁿ - 1)/(r - 1)
Sum of infinite series is given by a/(1 - r) where -1 < r < 1
Common Ratio = 36/9 = 144/36 = 576/144 = 2304/576
=> Common Ratio = 4 = 4 = 4 = 4
Hence, Common Ratio of the associated geometric sequence is 4
correct option is D) 4
( You Question lacks Table of Data but probably Table attached is required one)
Additional Info:
Function is
y = 9 × 4ˣ⁻¹
or
y = (9/4) × 4ˣ
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