Question

Determine if the sequence is arithmetic. If it is, find the common difference, the explicit formula, and the recursive formula.

-3. 7. 17. 27. ...

Answer 1

see explanation

Explanation:

Note there is a common difference d between consecutive terms, that is

d = 7 - (- 3) = 17 - 7 = 27 - 17 = 10

This indicates the sequence is arithmetic with n th term

`a_(n)` = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = - 3 and d = 10, thus

`a_(n)` = - 3 + 10(n - 1) = - 3 + 10n - 10 = 10n - 13 ← explicit formula

The recursive formula allows a term to be found by adding d to the previous term, thus

`a_(n)` =
`a_(n-1)` + 10 ← recursive formula