Question

A recursive rule for an arithmetic sequence is


`a_(1) = - 3i \: a_(n) = a_(n - 1) + 7`
What is the explicit rule of this sequence?
Note; The "i" in the equation is supposed to be a ";"

Answer 1

From the recursive rule, you have

`a_2=a_1+7`

`a_3=a_2+7=a_1+7(2)`

`a_4=a_3+7=a_1+7(3)`

`a_5=a_4+7=a_1+7(4)`

and so on. The general pattern for the
`n`-th term is adding
`n-1` copies of 7 to
`a_1`:

`a_n=a_1+7(n-1)`

With
`a_1=-3`, the sequence is explicitly given by

`a_n=-3+7(n-1)=7n-10`