The sum of the second and third terms of a geometric sequence is 96. The sum to infinity of this sequence is 500. Find the possible values for the common ratio, r.

Let, first term be a and common ratio is r.

So,

Sum of series,

a = 500( 1 - r )

Therefore, the value of common ratio is 0.916 .

Hence, this is the required solution.

18

step-by-step explanation:

draw the shape and you will see that f and k are actually at adjacent vertices (points of the hexagon that are neighboring).   so find the distance between (1,2) and (4,2).   that is easy since (1,2) and (4,2) is just a vertical distance to count, which is 3.   it is a regular polygon which means all sides are congruent.   you have 6 sides (hexa) so multiply 6 by 3 to receive 18.