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# A certain 300-term geometric sequence has first term 1337 and common ratio of -1/2. How many terms of this sequence are greater than 1?

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A certain 300-term geometric sequence has first term 1337 and common ratio of -1/2. How many terms of this sequence are greater than 1?

Guest Feb 19, 2017
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We need to solve this for "N"

1337(1/2)^(N - 1) = 1

(1/2)^(N - 1)  = 1/1337

log (1/2)^(N - 1) = log (1/1337)

(N - 1) log(1/2)  = log(1/1337)

N - 1  =  log (1/1337)/ log (1/2)

N  = log (1/1337)/ log (1/2) + 1 ≈ 11.384

So....the 11th term  is 1337(-1/2)^(10)  ≈ 1.305

And the 12th term is 1337(-1/2)^11  =  -.653

And.....the odd terms from 1 - 11  inclusively  will be positive and > 1....and there are six of these

CPhill  Feb 20, 2017

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