Answer:
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))
