Question

Find the explicit rule for the sequence: -4,1,6,11,...

Answer 1

f(n)=5n-9

Step-by-step explanation:

Given the sequence

`-4,1,6,11,...`
`\begin{gathered} 1-(-4)=1+4=5 \\ 6-1=5 \\ 11-6=5 \\ \implies\text{Common difference, d=5} \end{gathered}`

The explicit rule of an arithmetic sequence is obtained using the formula:

`\begin{gathered} f(n)=f(1)+(n-1)d \\ \text{where f(1)=first term} \end{gathered}`

Substituting, we have:

`\begin{gathered} f(n)=-4+5(n-1) \\ =-4+5n-5| \\ =-4-5+5n \\ f(n)=5n-9 \end{gathered}`

The explicit rule for the sequence is f(n)=5n-9.