Answer:
The next term is - 2 ⇒ last answer
Step-by-step explanation:
∵ The sequence is 54 , -18 , 6 , ......
∵ -18 ÷ 54 = [tex]-\frac{1}{3}[/tex]
∵ 6 ÷ -18 = [tex]-\frac{1}{3}[/tex]
- There is a constant ratio between each two consecutive terms
∴ The sequence is a geometric sequence
The nth rule of the geometric sequence is [tex]a_{n}=a(r)^{n-1}[/tex] , where
- a is the first term
- r is the constant ratio between each two consecutive terms
∵ The first term = 54
∴ a = 54
∵ The constant ratio = [tex]-\frac{1}{3}[/tex]
∴ r = [tex]-\frac{1}{3}[/tex]
∵ The next term is the fourth term
∴ n = 4
- Substitute a, r and n in the rule above
∴ [tex]a_{4}=54(-\frac{1}{3})^{4-1}[/tex]
∴ [tex]a_{4}=54(-\frac{1}{3})^{3}[/tex]
∴ [tex]a_{4}=54(-\frac{1}{27})[/tex]
∴ [tex]a_{4}=-2[/tex]
The next term is - 2
