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

#1**0 **

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