Question

Which function defines the sequence 6, 8, 10,…? Please explain this thoroughly

Answer 1

Given:-

`6,8,10,\ldots`

To find:-

The sequence in it.

Since the sequence is 6 for 1st term and 8 for 2nd term and 10 for 3rd term.

So the sequence is,

`2n+4`

The required sequence is 2n+4.

Now when n=1. we have,

`\begin{gathered} 2(1)+4=2+4 \\ \text{ =6} \end{gathered}`

When n=2. we have,

`\begin{gathered} 2(2)+4=4+4 \\ \text{ =8} \end{gathered}`

When n=3. we have,

`\begin{gathered} 2(3)+4=6+4 \\ \text{ =10} \end{gathered}`

So from this we can conform that the sequence is 2n+4.