Solving Sequences

Question

A_n= 4a_n-1 + 1/2

If the 3rd term in the sequence is 322.5, what is the value of the second term?

The answer is 80.5, but I am looking for HOW to solve this:

322.5 = 4a₂ + 1/2

Answer 1

If you subtract 1/2 from each side, you have 322 = 4a₂. Now all you have to do is divide by 4 to solve for a₂

Answer 2

322.5 = 4a₂ + 1/2 subtract 1/2 from both sides

322.5 - 1/2 = 4a_{2 reverse the sides}

4a₂ = 322.5 - 1/2 1/2=0.5

4a₂ = 322.5 - .5 = 322 divide both sides by 4

a₂ = 322/4 = 80.5

3rd term = 4 times 2nd term + 1/2

322.5 = 4a₂ + 1/2

322.5 = 4(80.5) + 1/2

= 322 + 1/2

=322.5