Question

A sequence is defined by the recursive formula f(n + 1) = 1.5f(n). Which sequence could be generated using the formula? –12, –18, –27, ... –20, 30, –45, ... –18, –16.5, –15, ... –16, –17.5, –19, ...

Answer 1

Answer:

The sequence -12 , -18 , -27 , ............ is generated using the formula ⇒ 1st sequence

Step-by-step explanation:

The recursive formula of the sequence is f(n + 1) = 1.5 f(n)

That means there is a constant ratio 1.5 between each two consecutive terms

In sequence -12 , -18 , -27 , ............

The first term is -12

The formula is f(n + 1) = 1.5 f(n)

Use the first term where n = 1 to find the 2nd term

∵ f(1) = -12

- Substitute n by 1 in the given formula

∵ f(1 + 1) = 1.5 f(1)

∴ f(2) = 1.5(-12)

∴ f(2) = -18

Use the second term where n = 2 to find the 3rd term

∵ f(2) = -18

- Substitute n by 2 in the given formula

∵ f(2 + 1) = 1.5 f(2)

∴ f(3) = 1.5(-18)

∴ f(3) = -27

∴ The sequence -12 , -18 , -27 , ............ is generated using the formula