Find the next term in the pattern and then write a rule for the nth term.

Question

1. 1/5, 2/10, 3/15, 4/20, ...

Answer 1

a_n = n / 5n

a₅ = 5 / 5(5)

a_n = ?

Answer 2

Looking at the first term, we can see that the pattern starts with 1/5. From there we can figure out what the relationship between the first term and the second term is. In this case, it looks like the second time is equivalent to n1 in terms of value, but it is written with 2 as the numerator instead of 1, so the denominator must also be multiplied by 2 for the values of n1 and n2 to remain equal.

The same is done for n3. n3 is again equal to n1, except that the numerator is 3, so the denominator must be 5 multiplied by 3, or 15.

When we get to n5, we do the same thing we have previously been doing. We know that the numerator must be 5, therefore the denominator must be 5 multiplied by 5, or 25. So the next value answer is 5/25. A rule for the nth term could be that we must multiply the numerator and denominator of 1/5 by whatever n is.