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dylanjones6996
23.05.2021 •
Mathematics
Write an explicit formula for a_na n , the n^{\text{th}}n th term of the sequence 5, -25, 125,
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Ответ:
Step-by-step explanation:
First, let's analyze the sequence.
We start with a 5.
Then, we get -25
We know that 25 is 5^2, and there is also a change of sign.
Then, we get 125.
We again know that 125 = 25^2, and again we have a change of sign.
So we will have something like:
Where the (-1)^n part is the responsible for the change of sign.
If we have:
a₁ = 5
Then:
a₂ = (-1)^3*(a₁)^2 = -1*(5)^2 = -25
as expected.
and:
a₃ = (-1)^4*(a₂)^2 = 1*25^2 = 125
as expected.
Then we can conclude that the explicit formula for the Nth therm is:
And if we want to write this in a more general way, we can rewrite this as:
Where we removed the necessity of knowing the previous term.
Ответ:
it is c
Step-by-step explanation: