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Expert: Sherman D. - 12/5/2008


Question
fifth and eighth terms of a geometric series are 540 and 20
respectively.

Using appropriate formulae, find

1. the first term and the common ratio   

my answer:

a = 43740, k = 1/2

2. the value to which the series converges
my answer:
a / (1 - k) = 65610

Thank you

Answer
the formula to use is

a(n) = a1 * r^(n - 1)

a(5) = a1 * r^(5 - 1)
540 = a1 * r^4

a(8) = a1 * r^(8 - 1)
20 = a1 * r^7

a1 = 540/(r^4) = 20/(r^7)

540r^7 = 20r^4
27 = r^(-3)
or
1/27 = r^3
r = (1/3)

a1 = 20/((1/3)^7)
a1 = 20/(1/2187) or 43740

1.)
it should be k = (1/3) not (1/2).

----------------------------

since your k is less than 1, your answer to #2 is correct.

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Sherman D.

Expertise

I can answer questions dealing in mathematics of all kinds except for Physics and Calculus, but i can answer questions in Pre-Calculus and Chemistry. I can also answer questions in Recipes of all kinds. I can find games cheats/walkthroughs, but i can`t find a specific game online or offline. I can also do history and recipes for alcoholic beverages.

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Mathematics, Recipes, History, and Games.

Education/Credentials
High School graduated. I graduated with honors, and i was in Beta Club for a year and a half.

Awards and Honors
Principle's list and A and B honor roll in high school only.

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