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Geometric Sequences











































Jack calls 4 people within 10 minutes of his son's birth to pass along the news. They each pass along the news to 4 new people within 10 minutes and so on. How many people have heard the news in 1 hour?

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Apr 04, 2013
Sequence
by: Staff


Answer

Part I


Any term in a geometric sequence can be computed using the following formula:

Geometric Sequence -Formula for the nth term in a sequence



The sum of n terms in a geometric sequence can be computed using the following formula:

Geometric Sequence - Formula for the sum of n terms in geometric sequence




an = a with a subscript of n is the nth term in the sequence

Sn = S with a subscript of n is the sum of the terms of the geometric sequence from n = 1 through the nth term in the sequence

a1 = a with a subscript of 1 is the 1st term in the sequence

n = number of terms

r = the common ratio

r, the common ratio, can be calculated as follows:
rn = an / an-1

(n must be greater than 1)


a1 = 4 (10 min)

a2 = 16 (20 min)

a6 = unknown (60 min)


Calculate rn

Common Ratio Calculation - Geometric Series





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Apr 04, 2013
Sequence
by: Staff


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Part II

Calculate how many people have heard the news in 1 hour

a1 = 4

r = 4

n = 6

Geometric Sequence - Calculate the sum of the first 6 terms




Final Answer:

Geometric Sequence - Final Answer - the sum of the first 6 terms








Thanks for writing.

Staff
www.solving-math-problems.com



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