Question

Write a recursive formula: 3, 5, 7, 9, 11, 13, 15, 17, 19, 21

Answer 1

`a_1=3`

`a_n=a_n_-_1+2`

Explanation:

Recursive formula : an = a(n-1) + d

where d = common difference , an = nth term, and n = number of terms

Because we are just writing the recursive formula rather than the explicit formula, the only defined term will be "d" or the common difference.

Here, the common difference is +2. This is evident as you must add 2 to get to 5 and then add 2 to get to 7 etc.

So d = 2

Plugging this into the recursive formula we get an = a(n-1) + 2

Also it's very important to state the first term which is 3 so a1 = 3