In a geometric sequence, the nth term is given by.......
an=a1(r)n-1 where.....
r=(an+1)/an
Our sequence terms are represented by...
a1=256
a2=64
a3=16
Let's calculate "r" if n=1.....
r=(a1+1)/a1
r=a2/a1
r=64/256.........substitute sequence values for a1,a2...
∴ r=1/4
Substitute "r =1/4" and "a1=256" into the general form for
geometric sequence expression...
an=256(1/4)n-1
Let's check our values using this equation...
a1=256(1/4)1-1.......n=1
a1=256(1/4)0
a1=256(1)
∴ a1=256.........√check, 1st term in sequence
a2=256(1/4)2-1.......n=2
a2=256(1/4)1
∴ a2=64............√check, 2nd term in sequence
Continuing checking several more terms.
