SOLUTION: Can someone help me? A sequence {g n} is defined recursively as g 1=72, g n=-2/3*g n-1 , for n ≥2 (note: here "n" & "1"& "n-1" after "g" should be a smaller letter, I can

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Question 1090885: Can someone help me?
A sequence {g n} is defined recursively as g 1=72, g n=-2/3*g n-1 , for n ≥2
(note: here "n" & "1"& "n-1" after "g" should be a smaller letter, I cannot put it here as smaller)
a. Determine the values of g 2, g 3, and g 4
b. Write an explicit formula for g n
Thank you.

Answer by KMST(5328)   (Show Source): You can put this solution on YOUR website!
I believe you meant and .

a) -->










b) is the general explicit formula for a geometric sequence with first term and common ratio .
For the sequence in this problem,
,
That is "an explicit formula" for .
As , the formula could be "simplified"



That last equation is also "an explicit formula" for .
As a formula it may not look simple,
but it would help if you had to calculate several terms,
because it would simplify calculations like
, and
.

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