Question

Find the common difference and the recursive formula. 22,19,16,13

Answer 1

`22,19,16,13`

The common difference between each term is -3.

19 - 22 = -3

16 - 19 = -3

13 - 16 = -3

The recursive formula of an arithmetic sequence follows the pattern below:

`a_n=a_(n-1)+d,n\ge2`

where d = common difference and number of terms "n" must be more than or equal to two.

To be able to get the recursive formula, we will plug in the common difference assuming that first term a₁ = 22. Therefore, the recursive formula is:

`a_n=a_(n-1)-3,for\text{ n}\ge2`