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Expert: Sherman D. - 9/19/2008


Question
Hi Sherman,
I have a question:
a, 3a,...
The first term in the sequence above is a, and each term after the first is 3 times the preceding term. If the sum of the first 5 terms is 605, what is the value of a? I got 25 but the correct answer is 5. Why? THanks in advance

Answer
a, 3a, 3(3a), 3(3(3a)), 3(3(3(3a)))

or you can write it as

(3^(n - 1))a

this would be a geometric sequence

a(n) = a * 3^(n - 1)

the summation for this is

S(n) = (a(1 - 3^n))/(1 - 3)

S(5) = (a(1 - 3^5))/-2

605 = (242/2)a
605 = 121a
a = 6

Proof

a + 3a + 9a + 27a + 81a = 605
121a = 605
a = 5

Info found at www.mathguide.com/lessons/SequenceGeometric.html

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Sherman D.

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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.

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

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

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