Write a formula for the general term or nth term for the sequence. Then find the indicated term. three fourths comma three sixteenths comma StartFraction 3 Over 64 EndFraction comma StartFraction 3 Over 256 EndFraction ...; a 8

Sequence: 3/4, 3/16, 3/64, 3/256

a8=?

a1=3/4

a2=3/16

a3=3/64

a4=3/256

a2/a1 = (3/16) / (3/4) = (3/16) * (4/3) = 4/16=1/4

a3/a2 = (3/64) / (3/16) = (3/64) * (16/3) = 16/64=1/4

a4/a3 = (3/256) / (3/64) = (3/256) * (64/3) = 64/256=1/4

a2/a1=a3/a2=a4/a3=r=1/4

an=a1*r^ (n-1)

an = (3/4) * (1/4) ^ (n-1)

an = (3/4) * (1) ^ (n-1) / (4) ^ (n-1)

an = (3/4) * (1/4^ (n-1))

an = (3*1) / [4*4^ (n-1) ]

an=3/4^ (1+n-1)

an=3/4^n

n=8→a8=3/4^8

a8=3/65,536

Answers:

The general term or nth term for the sequence is: an=3/4^n

a8=3/65,536