First solution:

Let's write down the expressions for and using the formula of the general term of the sequence:


Note is unknown in both equations (1) and (2). Subtract from both sides of (2) and then on the right side of this equality replace by its expression from (1).



So
Then substitute the known values

Strategy

In solving these problems it's important to carefully analyze the formulas and use transformations to avoid unnecessary calculations. For example, in the problem we got rid of by subtracting one equality from another.

Useful formulas:

Let A and B be algebraic expressions such as . Then
(symmetry);
(adding u);
(subtracting u);