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Find an explicit formula for the geometric sequnce a1=15 and a3=135

 May 7, 2021
 #1
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Same thing as last time. Pull out 15 from both - a1 = 1, a3 = 9.

 

Ask: What can I multiply 1 by twice to get 9?

\(1 * x * x = 9\)

\(9 = x^2, x = 3\)

 

Okay so if a geometric equation is of form:

\(y=ab^x\)

Then a = 15 (what we pulled out to make the problem easier to solve) and b = 3

\(y = 15(3^x)\)

 May 7, 2021
 #2
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+1

a1 * r * r  = a3

15 r^2 = 135

r^2 = 9

r = 3

 

an = a1 (3n-1)

an = 15 * 3n-1

 May 7, 2021

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