The explicit formula for the geometric sequence Negative one-ninth, one-third, negative 1, 3, negative 9, ellipsis is f (x) = negative one-ninth (negative 3) Superscript x minus 1. What is the common ratio and recursive formula for this sequence?
Answers
Answered by
6
common ratio = -1/3 &
recursive formula f(x) = (-1)ˣ(3)ˣ⁻³
Step-by-step explanation:
f(x) = -(1/9)(-3)ˣ⁻¹
-1/9 , 1/3 , - 1 , 3 , - 9
Common Ratio = (1/3)/(-1/9) = -1/(1/3) = 3/(-1) = -9/3 = - 3
Common Ratio = - 3
First term = -1/9
Nth Term = First Term * ( Common Ratio)ⁿ⁻¹
=> nth term = (-1/9) * (-3)ⁿ⁻¹
=> nth term = -(1/3)² * (-3)ⁿ⁻¹
=> nth term = -(3)⁻² * (-3)ⁿ⁻¹
=> nth term = -(-3)ⁿ⁻³
=> nth term = -(-1)ⁿ⁻³(3)ⁿ⁻³
=> nth term = (-1)ⁿ⁻²(3)ⁿ⁻³
=> nth term = (-1)ⁿ(3)ⁿ⁻³
=> f(x) = (-1)ˣ(3)ˣ⁻³
Answered by
130
Answer:
bro its b
Step-by-step explanation:
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