Question

The second and third terms in the following Fibonacci sequence are x and y. Write down algebraic expressions for the first, fourth and fifth terms.

*blank*, x, y, *blank*, *blank*

Answer 1

Let the first term be a

Taking the second and third terms to be x and y.

Then third term =first term +second term

=a+x

From the word problem , a+x=y

first term(a) =y-x

Therefore the fourth term =third term +second term =y+x

The fifth term =fourth term +third term =(y+x)+y =2y+x

Hence;First term =y-x

Fourth term =y+x

Fifth term =2y+x