+939 A geometric sequence has 400 terms. The first term is 1000 and the common ratio is -\frac{8}{9}$ How many terms of this sequence are greater than 1?
+130097 Only the odd terms can be positive.....so (-8/9)^(n-1) = (8/9)^(n-1) when n is odd
We need to solve this
1000 (8/9)^(n -1) > 1 divide both sides by 1000
(8/9)^(n-1) > 1/1000 take the log of both sides
log (8/9)^(n-1) > log (1/1000) and we can write
(n-1) log (8/9) > log (1/1000) rearrange as
n < log ( 1/1000) /log (8/9) + 1 we divided by a negative - log (8/9) - so, reverse the inequality sign
n < ≈ 59.6
The 59th term is the last one > 1
So....the number of terms > 1 = 60/2 = 30
