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rcherala
18.03.2020 •
Mathematics
Find an explicit rule for the geometric sequence using subscript notation. Use a calculator and round your answers to the nearest tenth if necessary.
The third term of the sequence is 150. The fifth term is 96.
The explicit rule for the geometric sequence is an =
(
)n − 1.
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Ответ:
a_n = 234.38 * (0.8 ^ (n - 1))
Step-by-step explanation:
We have that the geometric sequence has the form of:
a_n = a * (r ^ (n - 1))
Now, we know that the third term has a value of: 150
And that the fifth term has a value of: 96
We know that the third term has the following form:
a_3 = a * (r ^ 2) = 150
And the fifth term has the following form:
a_5 = a * (r ^ 4) = 96
Therefore we have equations, if we divide both equations that is to say a_3 / a_5, we have to:
a * (r ^ 2) / a * (r ^ 4) = 150/96
The term a is canceled and we are left with:
1 / r ^ 2 = 1.5625
solving for r, we are left with:
r = (1 / 1.5625) ^ (1/2)
r = 0.8
Now to know the value of a, we use the following equation:
a_3 = a * (r ^ 2) = 150
we replace r and we are left with:
a * (0.8 ^ 2) = 150
a = 150 / (0.8 ^ 2)
a = 234,375
Therefore, we know all the terms and we can complete the equation:
a_n = 234.38 * (0.8 ^ (n - 1))
Ответ:
on what
Step-by-step explanation: