Question

A sequence is shown below.10, 12, 14, 16, ...Which function can be used to determine the nthnumber in the sequence?

Answer 1

The nth term of the given sequence can be determined using the function;

`a_n=2n+8`

Step-by-step explanation:

Given the sequence;

`10,12,14,16,\ldots`

The sequence is an arithmetic progression with a common difference d and first term a;

`\begin{gathered} d=12-10 \\ d=2 \\ a=10 \end{gathered}`

Recall that the nth term of an AP can be calculated using the formula;

`a_n=a+(n-1)d`

substituting the given values;

`\begin{gathered} a_n=a+(n-1)d \\ a_n=10+(n-1)2 \\ a_n=10+2(n-1) \\ a_n=10+2n-2 \\ a_n=2n+10-2 \\ a_n=2n+8 \end{gathered}`

Therefore, the nth term of the given sequence can be determined using the function;

`a_n=2n+8`