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A geometric sequence has 400 terms. The first term is 1000 and the common ratio is \(-\frac{1}{3}\) How many terms of this sequence are greater than 1?

 Apr 9, 2024
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Only the odd terms are positive

 

So

 

1000*(1/3)^(n -1 )  > 1      

 

(1/3)^(n-1)  >  1/1000  take the log of both sides

 

(n -1) log (1/3)  > log (1/1000)                   (log 1/3  is  negative....reverse the sign )

 

n -1 <  log (1/1000) /(log (1/3)

 

n < 1  + log (1/1000) /log (1/3)

 

n < 7.28

 

The 1st , 3rd, 5th and  7th terms will all be  > 1  ........4 terms

 

cool cool cool

 Apr 9, 2024

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