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

Answer:

see explanation

Step-by-step explanation:

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

r = $\frac{18}{24}$ = $\frac{3}{4}$ = 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$(0.75)^{n-1}$