Write a formula for the general term or nth term for the sequence. Then find the indicated term. five halves comma five fourths comma five eighths comma five sixteenths ...; a 8 a Subscript nequals?

Sequence: 5/2, 5/4, 5/8, 5/16

a8=?

a1=5/2

a2=5/4

a3=5/8

a4=5/16

a2/a1 = (5/4) / (5/2) = (5/4) * (2/5) = (5*2) / (4*5) = 2/4=1/2

a3/a2 = (5/8) / (5/4) = (5/8) * (4/5) = (5*4) / (8*5) = 4/8=1/2

a4/a3 = (5/16) / (5/8) = (5/16) * (8/5) = (5*8) / (16*5) = 8/16=1/2

Ratio: r=a2/a1=a3/a2=a4/a3→r=1/2

an=a1*r^ (n-1)

a1=5/2, r=1/2

an = (5/2) * (1/2) ^ (n-1)

an = (5/2) * [1^ (n-1) / 2^ (n-1) ]

an = (5/2) * [1/2^ (n-1) ]

an = (5*1) / [2*2^ (n-1) ]

an=5/2^ (1+n-1)

an=5/2^n

n=8→a8=5/2^8

a8=5/256

Answers:

The formula for the general term or nth term for the sequence is an=5/2^n

a8=5/256