SOLUTION: 2. The first three terms of a geometric sequence are ln x^16, ln x^8, ln x^4, for x>0. a. Find the common ratio. b. Solve {{{sum((2^(5-k)),k=1,infinity)*ln(x)}}}{{{""=""}}}{

Algebra ->  Functions -> SOLUTION: 2. The first three terms of a geometric sequence are ln x^16, ln x^8, ln x^4, for x>0. a. Find the common ratio. b. Solve {{{sum((2^(5-k)),k=1,infinity)*ln(x)}}}{{{""=""}}}{      Log On

a1 = ln(x16) = 16∙ln(x) 
a2 = ln(x8) = 8∙ln(x)
a3 = ln(x4) = 4∙ln(x)

r = a2/a1 = 8∙ln(x)/16∙ln(x) = 1/2

First we find:

 

a1 = 25-1 = 24 = 16
a2 = 25-2 = 23 = 8

r = a2/a1 = 8/16 = 1/2



Then 



becomes







raise e to the powers of both sides





Edwin