Question

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

Answer 1

Answer:

see explanation

Step-by-step 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