Question

A geometric sequence is defined by the equation an = (4)3 − n. part

a.what are the first three terms of the sequence? (1 point) part
b.what is the value of r? part
c.what is the value of a12?

Answer 1

a. an=4^(3-n)
a1= 4^(3-1) = 4^2 = 16
a2= 4^(3-2) =4^1 = 4
a3= 4^(3-3) = 4^0 = 1
b. r= 1/4 (you can see from what I prove in the picture or from part a
an= a1r^(n-1)
4 = 16(r)^(2-1)
4 = 16(r)
so r = 4/16 = 1/4
c. a12=a1r^(n-1)
=16(1/4)^(12-1)
=16(1/4)^11
=16/ 4^11
=16/4194304
=3.81*10^(-5)