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