The given pattern continues. Write down the nth term of the sequence ​asubn suggested by the pattern. 1 Over 18, 2 Over 19, 3 Over 20, 4 Over 21...

Answer 1

We know the following:

a₁ = 1/18

a₂ = 2/19

a₃ = 3/20

and so on...

So, what is the pattern here? Well, the numerator and denominator each increase by 1 for each next term in the sequence. So we can conclude the following:

a_n = 1 + (n-1) / 18 + (n-1)

We need to use (n-1) instead of just n because otherwise we would not be starting from a₁, we would be starting at a₂. I recommend testing this out with plugging in 1 for n to see this.

By simplifying our equation, we get that

a_n = n / (17 + n)