The infinite sequence S = {s_1, s_2, s_3, ...} is defined by s_1 = 7 and s_n = 7*s_{n - 1} for each integer n > 1 . What is the remainder when s_{100} is divided by 3?
+2666 Notice how the value of the \(n\)th term is \(7^n\).
This means that the 100th term will be \(7^{100}\).
Now, notice that the remainder when \(7^{100}\) is divided by 3 is the same as the remainder when 7 is divided by 3.
Can you take it from here?
