Question

What is the next term in the following sequence? 54, -18, 6, ... 3 2 -3 -2

Answer 1

Answer:

D. -2

Step-by-step explanation:

Hope it helped UwU

Answer 2

Answer:

The next term is - 2 ⇒ last answer

Step-by-step explanation:

∵ The sequence is 54 , -18 , 6 , ......

∵ -18 ÷ 54 = $-\frac{1}{3}$

∵ 6 ÷ -18 = $-\frac{1}{3}$

- There is a constant ratio between each two consecutive terms

∴ The sequence is a geometric sequence

The nth rule of the geometric sequence is $a_{n}=a(r)^{n-1}$ , 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 = $-\frac{1}{3}$

∴ r =  $-\frac{1}{3}$

∵ The next term is the fourth term

∴ n = 4

- Substitute a, r and n in the rule above

∴ $a_{4}=54(-\frac{1}{3})^{4-1}$

∴ $a_{4}=54(-\frac{1}{3})^{3}$

∴ $a_{4}=54(-\frac{1}{27})$

∴ $a_{4}=-2$

The next term is - 2