SOLUTION: The first term of a geometric progression is 5 and the fifth term is 1280 find the common ratio of the progression.? Can I be shown step by step please as I need to be explained

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Question 1026926: The first term of a geometric progression is 5 and the fifth term is 1280 find the common ratio of the progression.?
Can I be shown step by step please as I need to be explained this in detail as I do not understand.

Found 2 solutions by ikleyn, MathTherapy:
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
The first term of a geometric progression is 5 and the fifth term is 1280 find the common ratio of the progression.?
Can I be shown step by step please as I need to be explained this in detail as I do not understand.
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Use the formula for the n-th term of geometric progression

a%5Bn%5D = a%5B1%5D%2Ar%5E%28n-1%29.

With the given data, you have 

1280 = 5%2Ar%5E4  --->  r%5E4 = 1280%2F5 = 256  --->  r = root%284%2C256%29.

This fourth root has 4 values in the complex domain, but if you need only real values, they are +/- 4.


Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
The first term of a geometric progression is 5 and the fifth term is 1280 find the common ratio of the progression.?
Can I be shown step by step please as I need to be explained this in detail as I do not understand.
The formula for a specific term in a GP is: a%5Bn%5D+=+a%5B1%5Dr%5E%28n+-+1%29, where:
a%5Bn%5D is the value of the term
a%5B1%5D is the value of the 1st term
n is the term number
For the 5th term, a%5Bn%5D+=+a%5B1%5Dr%5E%28n+-+1%29 becomes:
a%5B5%5D+=+5r%5E%285+-+1%29
matrix%281%2C3%2C+%221%2C280%22%2C+%22=%22%2C+5r%5E4%29
matrix%281%2C3%2C+%221%2C280%22%2F5%2C+%22=%22%2C+r%5E4%29
256+=+r%5E4
r+=+root+%284%2C+256%29