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avatar+214 

  { \(a_n\)} is a geometric sequence with common ratio r > 0. If \(a_1\)= 1, \(6a_n\)\(a_{n+1}+a_{n+2}\), then find the sum of the first 4 terms of { \(a_n\)} .

 #1
avatar+128794 
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a = 1

6a = a2 + a3

6 = a2 +a3

6 = ar + ar^2

6 = 1r + 1r^2

6 = r + r^2

r^2  + r  -  6 =  0

(r - 2) ( r + 3)  =  0

r - 2 =  0 

r =  2

 

So

 

S4  =   1 + 2 + 2^2 + 2^3  =   15

 

cool cool cool

 Apr 7, 2024
 #2
avatar+214 
+1

Thanks so much CPhill, you are a really good answerersmiley


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