+280 A geometric sequence has 400 terms. The first term is 1000 and the common ratio is \(-\frac{1}{3}\) How many terms of this sequence are greater than 1?
+129846 Only the odd terms are positive
So
1000*(1/3)^(n -1 ) > 1
(1/3)^(n-1) > 1/1000 take the log of both sides
(n -1) log (1/3) > log (1/1000) (log 1/3 is negative....reverse the sign )
n -1 < log (1/1000) /(log (1/3)
n < 1 + log (1/1000) /log (1/3)
n < 7.28
The 1st , 3rd, 5th and 7th terms will all be > 1 ........4 terms
