Choosing APs from a GP
Algebra
Level
pending
What is the number of increasing APs of length at least that can be chosen from an infinite GP having common ratio ?
Infinitely Many
r
Zero
1
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
It can be easily checked that a , a r 2 , a r 3 are in AP. Thus multiplying these three terms by a r m and then varying m over the set of natural numbers, we get infinitely many APs.