For the following geometric sequence find the recursive formula and the 5th term in the sequence. In your final answer, include
2 answers:
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Answer:
Amount she Receive in 5 years = $3506.37
Step-by-step explanation:
Given in question as
Ebonie invests amount in account = P = $2500
The interest rate she will have = 7%
The amount will keep in account for 5 years
Now we apply compound interest (CI ) to determine how much she will receive after 5 years ,
So , for CI
Amount = principal ( 1 + ^ T ,where T is Time
So, A = 2500 ( 1 +)^5
Or, A = 2500 (1.40255)
Or, A = $3506.37
Hence Amount she will receive $ 3506.37 Answer
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Answer:
a) x = (√5 -1)/2 ≈ 0.618034
b) 1/x = (√5 +1)/2 ≈ 1.618034
Step-by-step explanation:
<u>Given</u>:
x/(1 -x) = 1/x
<u>Find</u>:
Exactly, and as a decimal approximation, ...
a) x, using the quadratic formula
b) 1/x
<u>Solution</u>:
a) We can multiply the given equation by x(1 -x) to obtain ...
x² = 1 -x
x² +x -1 = 0 . . . . . . add x-1
The coefficients for use in the quadratic formula are a=1, b=1, c=-1. The solution using the quadratic formula is ...
We are only interested in the positive solution, which is ...
__
b) The quadratic we developed in the first part can be rearranged like this:
x² +x = 1 . . . . . . add 1 to both sides
x(x +1) = 1 . . . . . factor out x
x +1 = 1/x . . . . . .divide by x
Then to find the value of 1/x, we simply need to add 1 to the value of x we have: