Question

Find the next three terms of the given sequences below. Type your answer on the blank.1. 12, 18, 24, 30, 36,2.90, 81, 72, 63, 543.100, 90, 80, 70,

Answer 1

We have three arithmetic sequences. Arithmetic sequences have a common difference between each consecutive terms. We just have to calculate the common difference of each sequence and then add to the last term to get the following terms.

item a)

The common difference is

`18-12=6`

The next three terms are

`\begin{gathered} 36+6=42 \\ 42+6=48 \\ 48+6=54 \end{gathered}`

42, 48 and 54.

item b)

The common difference is

`81-90=-9`
`\begin{gathered} 54+(-9)=45 \\ 45+(-9)=36 \\ 36+(-9)=27 \end{gathered}`

The next three terms are 45, 36 and 27.

item c)

The common difference is

`90-100=-10`
`\begin{gathered} 70+(-10)=60 \\ 60+(-10)=50 \\ 50+(-10)=40 \end{gathered}`

The next three terms are 60, 50 and 40.