+1367 A geometric sequence has $400$ terms. The first term is $500$ and the common ratio is $-\frac{1}{20}.$ How many terms of this sequence are greater than $1?$
+129630 We want to solve this
500 (1/20)^(n -1) > 1 divide both sides by 500
(1/20)^(n -1) > 1/500 take the log of both sides and we can wtite
(n -1) log (1/20) > log (1/500)
{divide both sides by log (1/20)...since thisis negative, reverse the inequality sign }
n -1 < log (1/500) / log (1/20)
n < [ 1 + log (1/500) /log (1/20) ]
n < 3.07
The first three terms will be > 1
