write an expression for the apparent nth term of the sequence. (assume that n begins with 1.) 2/2, 3/5, 4/8, 5/11, ...

Question

Please help :)

Answer 1

First let's just look at the pattern. It looks to me like our numerators are increasing by one and our denominators are increasing by three. We know that these increasing increments of 1 and 3 will become our coefficients.

 

If our numerator was a standalone sequence, we might write it as a_n=n+1

If our denominator was a standalone sequence, we might write it as a_n=3n-1

 

So our sequence as a whole will be an=(n+1)/(3n-1)