We can set this up as a Fibonacci Series
f1 =f1
f2 = f2
f3 = f2 + f1
f4 = 2f2 + f1
f5 = 3f2 + 2f1
f6 = 5f2 + 3f1
f7 = 8f2 + 5f1
f8 = 13f2 + 8f1
f9 = 21f2 + 13f1
f10 = 34f2 + 21fi
______________
Sum = 88f2 + 55f1
Using a Fibonacci identity...... 11f(5) = f(10)
So
11 [ 3f2 + 2f1] = 33f2 + 22f1 = 34f2 + 21f1 ⇒ f1 = f2
Then
f7 = 8f2 + 5f1
f7 = 8f1 + 5fi
f7 = 13f1 = 83
13f1 = 83
f1 = 83/13
And the sum of the series = 88f2 + 55f1 = 88f1 + 55f1 = 143 f1
So....the sum is 143 (83/13) = 913
Just as the Guest found !!!