The product of the first five terms of a geometric progression is 1024, and the fourth term is 2017. Find the second term.
+128475 Call the first term, N
Let the common ratio be , r
So
Nr^3 = 2017
N = 2017 / r^3
So we have that
( 2017/r^3) ( 2017/r^2) ( 2017/r) (2017) (2107 r) = 1024 simplify
(2017)^5 / r^5 = 1024
(2017)^5 /1024 = r^5 take the 5th root of both sides
2017/4 = r
The second term is
First term * r =
[ 2017 / ( (2017/4)^3 ] * (2017/4) = 16/2017
