Answer:
13, 21, and 34
Step-by-step explanation:
x(n) + x(n+1) + x(n+2)= 68
x(n), x(n+1), and x(n+2) are three consecutive Fibonacci numbers.
=> (x) + (x+k) + (x+x+k)=68
(x is a Fibonacci number and k is a positive integer)
=> 4x + 2k = 68
=> 2x + k = 34
=> x < 17
Check two Fibonacci numbers that are closest to 17 and smaller than 17.
x(n)=8 => x(n+1)=13, x(n+2)= 21
=>x(n) + x(n+1) + x(n+2)= 8 + 13 + 21 = 42 (not valid)
x(n) = 13 => x(n+1) = 21, x(n+2)= 34
=> x(n) + x(n+1) + x(n+2)= 13 + 21 + 34 = 68 (valid)
Hope this helps!
