The fifth term and the eighth term of a geometric progression are 27 and 729 respectively. What is its 11th term?

A girl counted in the following way on the fingers of her left hand: She started by calling the thumb 1, the index finger 2, middle finger 3, ring finger 4, little finger 5 and then reversed direction calling the ring finger 6, middle finger 7, and so on. If she counted up to 1994, on which finger did she end her counting?

For an infinite geometric progression a, ar, ar2, ar3, ... if the numerical value of common ratio |r| < 1, then the sum to infinity S∞ will be: