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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 $1?$

 Jun 18, 2024
 #1
avatar+129733 
+1

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

 

cool cool cool

 Jun 19, 2024

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