## Puzzle 90: Seed Numbers

Consider two whole numbers (for example 3 & 6). These will be the first two numbers. The third number is the sum of the first two (9). The forth is the sum of the previous two (15), and so on (3, 6, 9, 15, 24, 39, …). What do the first two number have to be such that the fifth number is 100? Explain your strategy.

Extension: What is the equation to predict the seed numbers? Can you do the same for 200, 300, etc? What is your strategy and proof?

Extension: What is the equation to predict the seed numbers? Can you do the same for 200, 300, etc? What is your strategy and proof?