Geometric Sequences

Heartofali0n

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May 8, 2011
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So this was on a quiz, and i still have the chance to fix it. but i don't know how.
So I know how to solve for the 3 missing terms when there is 5 numbers, for example. 2, ___,___,___, 6
You use a formula that has you solve for the middle one, then the first one , and then the last. But How would you do that if the problem was like this(6 numbers)
2,___,____,___, 6,10 ?? the formula before was like this (for arithmetic sequences)

a3 = a1 +a5
________
2
a2 = a3 + a1
_________
2
a4 = a3 +a5
_______
2

that line with the 2 under is "divide by 2"
but I didn't know how to use that formula for 6 numbers AND the question on the quiz was for GEOMETRIC sequences.. not arithmetic.? HELP!? I can only think of Geometric mean. and solving by multiplying a1 and a6 (finding a3 ) and then a3 Multiply a1 and so on...
 
\(\displaystyle \sqrt{a_{1}\cdot a_{3}} = a_{2}\)
 
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