The arithmetic series is given by (k+1)+(2k+3)+(3k+5)+...+303. a)Find the number of term in the series in terms of k. b) Show that the sum of the series is given by (152k+46208)/(k+2). c)Given that S=2568, find k.

a) I would start by trying to see if the student can do it by himself. In the case the student does not know how to start, I would start by asking him if can find the general term. Here there are two ways to do it: you can either look at the first terms and see that the general term is nk+(2n-1) or you can start building it by the general formulas for arithmetic sequences a2=a1+d, where d is the difference between the terms. From here you just equate the general term to 303 and get 302/(k+2).b) For the second part, I would direct the student towards the formula for the sum of the arithmetic series s=n(a1+an)/2. By replacing the terms you can get to the desired form of the euation.c) The last part is a matter of getting what you have previously found and equate it to 2568. From here it is a matter of mathematical computation.