# Problem of the Week Problem C Teacher Road Trip 1

To help pass time on a long bus ride, $$35$$ math teachers created a sequence of numbers, with each teacher saying one term in the sequence. The first teacher said the number $$2$$, the second teacher said the number $$8$$, and every teacher after that said the sum of the two previous terms. Thus,

• the third teacher said the sum of the first and second terms, which is $$2+8=10$$, and

• the fourth teacher said the sum of the second and third terms, which is $$8+10=18$$.

Once the final teacher said their number, the 25th teacher announced they had made a mistake and their number should have been one more than what they had said. How much larger should the final teacher’s number have been?

Themes: Algebra, Number Sense