fibonacci problems? "If 8th number is 2017, what is largest possible value of 1st?"

[nanase]

Do you see that you can get another solution (with a larger value for a) by adding 13 to a and subtracting 8 from b? How far can you continue this?

Thank you for the hint & example Dr.Peterson, I quickly tried it again with trials and error and get a = 244 and b = 5, is this it?

 

[Dr.Peterson]

Thank you for the hint & example Dr.Peterson, I quickly tried it again with trials and error and get a = 244 and b = 5, is this it?

You don't really need trial and error at this point. Just divide and round down to get the 5: 149/8 = 18.625, so you can subtract 8 from 149, 18 times; 149 - 8*18 = 5. Then 10 + 13*18 = 244.