The third term of a sequence is 120. The fifth term is 76.8. Write an explicit rule representing this geometric sequence.

The nth term of the geometric sequence is:

an=ar^ (n-1)

where

a=first term

r=common ratio

n=nth term

from the question:

120=ar (3-1)

120=ar^2

a=120 / (r^2) ... i

also:

76.8=ar^ (5-1)

76.8=ar^4

a=76.8/r^4 ... i

thus from i and ii

120/r^2=76.8/r^4

from above we can have:

120=76.8/r²

120r²=76.8

r²=76.8/120

r²=0.64

r=âš0.64

r=0.8

hence: a=120 / (0.64) = 187.5 therefore the formula for the series will be: an=187.5r^0.8

The nth term of the geometric sequence is:

an=ar^ (n-1)

where

a=first term

r=common ratio

n=nth term

from the question:

120=ar (3-1)

120=ar^2

a=120 / (r^2) ... i

also:

76.8=ar^ (5-1)

76.8=ar^4

a=76.8/r^4 ... i

thus from i and ii

120/r^2=76.8/r^4

from above we can have:

120=76.8/r²

120r²=76.8

r²=76.8/120

r²=0.64

r=√0.64

r=0.8

hence:

a=120 / (0.64) = 187.5

therefore the formula for the series will be:

an=187.5r^0.8