The Fibonacci sequence is the sequence 1, 1, 2, 3, 5, $\ldots$ where the first and second terms are 1 and each term after that is the sum of the previous two terms. What is the remainder when the $100^{\mathrm{th}}$ term of the sequence is divided by 8?
Question:
The Fibonacci sequence is the sequence 1, 1, 2, 3, 5, $\ldots$ where the first and second terms are 1 and each term after that is the sum of the previous two terms. What is the remainder when the $100^{\mathrm{th}}$ term of the sequence is divided by 8?
Answer:
Let's think step by step.

user
3
The Fibonacci sequence is the sequence 1, 1, 2, 3, 5, $\ldots$ where the first and second terms are 1 and each term after that is the sum of the previous two terms. What is the remainder when the $100^{\mathrm{th}}$ term of the sequence is divided by 8?
train