Question

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

Answer 1

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