Write the following Arithmetic Sequence using a Recursive Formula: an = -5 + 2(n – 1)

Given:

To find:

The arithmetic sequence using a Recursive Formula.

Solution:

We have,

        ...(i)

The explicit formula of an AP is

        ...(ii)

where, a₁ is first term and d is common difference.

From (i) and (ii), we get

Now, the recursive formula of an AP is

Putting d=2, we get

Therefore, the arithmetic sequence using a Recursive Formula is defined as , where n>2 and .