Chapter 8.1, Problem 1MC

Student were asked to write an algebraic expression for the sum of five consecutive natural numbers .One student wrote $x+(x+1)+(x+2)+(x+3)+(x+4)=5x+10$. Another wrote $(x-2)+(x-1)+x+(x+1)+(x+2)=5x$.

a. Explain who is correct and why.

b. Does either approach prove that the sum of five consecutive integers equals 5 times the middle term?

c. Does the statement in part (b) generalize to the sum of consecutive term in every arithmetic sequence? Justify answer.