Question

Find the first term and the common difference of the arithmetic sequence described. Give a recursive formula for the sequence.Find a formula for the nth term.

Answer 1

Step 1:

The formula for  term is .

where is first term and is common difference.

term is .

   --------->  equation (1).

term is .

------->  equation (2).

Step 2:

Find , values by solving above two equations.

Subtract the equation (1) from (2).

Substitute  in equation (1).

.

Step 3:

The recursive formula is .

.

Substitute and in .

.

Solution:

The first term is .

The common difference is .

Recursive formula is .

The term is .