Question

How do you find the explicit formula for the following sequence 57, 66, 75, 84, 93, ...?

Answer 1

`n_(th)` of the series is given by `9n+48`

Explanation:

As the difference between a term and its preceding term is always `9`, it is an arithmetic sequence of type

`{a,a+d,a+2d,a+3d,a+4d,a+5d,..........}`

If `a` is the first term of such a series and `d` is the difference between a term and its preceding term,

`n_(th)` of the series is given by `a+(n-1)d`.

Here `a=57` and `d=9`, hence

`n_(th)` of the series is given by `57+9(n-1)=9n+48`.