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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?

 Jun 1, 2022
 #1
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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?

 Jun 1, 2022

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