If the numbers below form a geometric sequence, identify the 5th term in the sequence: 3, 4.5, 6.75, 10.125, ....

Question

A.) 15.1875 B,)11.625 C.)16.875 D.)This is not a geometric sequence, so the 5th term cannot be determined. *****Need answer!!!! please and thank you.*****

Answer 1

Start by looking at the change between numbers. It's easier if you look at the change as a fraction.

 

between 4.5 and 3 = 1.5 = 3/2

between 6.75 and 4.5 = 2.25 = 9/4

between 10.125 and 6.75 = 3.375 = 27/8

 

If you look at the change between the changes, you'll notice that the numerator increases by a factor of 3 and the denominator increases by a factor of 2. That is:

 

3/2 * (3/2) = 9/4

9/4 * (3/2) = 27/8

 

So, the next logical change will be:

 

27/8 * (3/2) = 81/16

 

Now add 81/16 to 10.125 and you get 15.1875.