Consider the statement that 3 divides /7 + 2n whenever n is a positive Integer. Outline the proof by clicking and dragging to complete each statement. Let P(n) be the proposition that Basis step: P(1) states that 3 divides n' + 2n. Inductive step: Assume that P(n) is true for all integers n = 1. 3 divided k' + 2k for an arbitrary integer k > 0. Show that () 'O A(K + 1) is true, thereby completing the Induction step. (k + 1) + 2(k + 1) = (k" + 3k# + 3k + 1) + (2k + 2) = (k* + 5k) + 3(k# + 1) By the inductive hypothesis, 3 divides (K* + 2k). 3 divides 3(k' + k + 1) because it is 3 times an integer. (k + 1) + 2(k + 1) = (k- + 343 + 3k + 1) + (2k + 2) = (K3 + 2k) + 3(k= + k+ 1) By the inductive hypothesis, 3 divides (K + 5k). 3 divides 3(k' + 1) because it is 3 times an integer. By part (i) of Theorem 1 in Section 4.1, 3 divides the sum (k* + 2k) + 3(k' + k + 1). This completes the inductive step