Write a recursive formula for the following sequence 25,43,61,79,97 F(1)= 25
F(n)= F (n-1) +18

Given:

The sequence is:

25,43,61,79,97

To find:

The recursive formula for the given sequence.

Solution:

We have,

25,43,61,79,97

Here, the first term is 25. Now, the differences between the two consecutive terms are:

The differences between the two consecutive terms is common, i.e., 18. So, the given sequence is an arithmetic sequence.

The recursive formula of an arithmetic sequence is:

Where, d is the common difference and F(1) is the first term.

Putting , we get

, where .

Therefore, the required recursive formula is , where .