SOLUTION: A geometric sequence has 400 terms. The first term is 1600 and the common ratio is 9/10. How many terms of this sequence are greater than 1?

Question 1209373: A geometric sequence has 400 terms. The first term is 1600 and the common ratio is 9/10. How many terms of this sequence are greater than 1?
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
The n-th term of the sequence is: a_n = 1600*(0.9)^(n-1)
A term will be equal to 1 if 0.9^(n-1) = 1/1600
To solve for n, we take the log of both sides:
(n-1)log(0.9) = log(1/1600)
n = log(1/1600)/log(0.9) + 1 = 71.02
a_71 = 1600*0.9^70 = 1.0025
a_72 = 1600*0.9^71 = 0.902
Thus, the first 71 terms are greater than 1

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