Answer:
The second term of the sequence is y-x
The fourth term of the sequence is 2y-x
The fifth term of the sequence is 3y-x
Explanation:
The next term of a Fibonacci sequence is generated by taking the sum of the 2 preceding value of the sequence. Given the the first and third term of a Fibonacci sequence to be x and y
x, _, y...
let the second term be a, fourth term be b and fifth term be c to have the sequence;
x, a, y, b, c...
According to the definition;
x+a = y... 1
a+y = b... 2 and;
y+b = c... 3
From equation 1, a = y-x
Substituting a = y-x into equation 2 to get b we have;
(y-x)+y = b
2y-x = b
b = 2y-x
Substituting b = 2y-x into equation 3 to get 'c'
y + 2y-x = c
3y-x = c
c = 3y-x
The second term of the sequence is y-x
The fourth term of the sequence is 2y-x
The fifth term of the sequence is 3y-x