Consider the sequence 2, 9, 18, 29, 42, what is the 50th term in the sequence?

Answer 1

The general term is given by a_k=(k+3)^2-7 for k=0,1,2,3,4,5,..... which follows from the formula

1+3+5+7+....+(2n-1)=n^2. Hence, the 50th term will be a_{49}=(52)^2-7=2704-7=2697.