Question

Consider the following sequence 24,18,..

Assuming the sequence is geometric,
write the next three terms.
24, 18,
b.
Write an explicit equation
representing the sequence above.

Answer 1

see explanation

Explanation:

Since the sequence is geometric then the common ratio (r) is

r =
`(18)/(24)` =
`(3)/(4)` = 0.75

To find the next term in the sequence, multiply the previous term by r

The next 3 terms are

18 × 0.75 = 13.5

13.5 × 0.75 = 10.125

10.125 × 0.75 = 7.59375

The n th term equation of a geometric sequence is

`a_(n)` = a
`(r)^(n-1)`

where a is the first term, that is a = 24, hence

`a_(n)` = 24
`(0.75)^(n-1)`