Question

Is 81 in the sequence with the nth term 4n+1? Explain

Answer 1

If you can divide 81 by 4 and end up with a remainder of 1, then yes, 81 is a part of your sequence.

To justify that, it helps to think about ways we can represent numbers in terms of quotients and remainders. For example, if we take 10/3, we’ll obtain the quotient 3 with a remainder of 1, so another way of writing 10 would be 3(3)+1. If we replace that second three with any integer n, 3n+1 represents *every number* that leaves us with a remainder of 1 when we divide it by 3.

By the same logic, 4n+1 represents every number that leaves a remainder of 1 when we divide it by 4. 81 indeed meets this requirement, since can be written as 4(20)+1, so it would be a part of the sequence.