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A geometric sequence has 400 terms.  The first term is 1000 and the common ratio is -\frac{9}{10}.  How many terms of this sequence are greater than 1?

 Jan 2, 2024
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(1000) (.9)^(n - 1)  =  1

 

.9^(n -1)n  = 1/1000      take the log of  both sides

 

log .9^n  = log (1/1000)

 

(n-1) log (.9)  =  log (1/10000

 

n -1 = log (1/1000) / log (.9) ≈  65.56

 

n = 65.56 + 1 =   66.56

 

66 terms will be > 1

 

cool cool cool

 Jan 2, 2024
edited by CPhill  Jan 2, 2024

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