Question

Write an explicit rule to represent the sequence :
4, 10, 16, 22,...

Answer 1

It's an arithmetic sequence:

`a_1=4;\ a_2=10;\ a_3=16;\ a_4=22;\ ...`

The explicit rule:

`a_n=a_1+(n-1)d`

`d=a_(n+1)-a_n\to d=a_2-a_1=a_3-a_2=a_4-a_3=...`

`d=10-4=16-10=22-16=6`

Substitute:

`f(n)=4+(n-1)(6)=4+6n-6=6n-2`

Answer: f(n) = 6n - 2