Question 21 18 pts Prove algebraically that for all integers x, the expression x3 + 3x2 + 5x has the same parity as x. (Remember that the parity of an integer refers to whether it's even or odd.) Edit View Insert Format Tools Table 12pt v Paragraph B I U Av & TV Q B B BV Q SV EV EV S D BV V VX CD p O words >Question 22 18 pts Consider a sequence an defined as follows: a1 = 50 an = 2an-1 + 10(n - 1) for n > 1 Let P(n) be the statement that an explicit formula for the nth term of this sequence is an = 70(20 - 1) - 10n - 10 We wish to prove P(n) by induction for all integer values of n > = 1. Basis step: We will show that P(1) is true. P(1) : a1 = 70(21-1) - 10(1) - 10 = 70 - 10 - 10 = 50. This matches the value of a1 given in the sequence. Inductive step: Let k >= 1, and assume that P(k) is true. We must show that P(k + 1) is true. Complete the rest of the inductive step below. Be sure to: . Define the inductive hypothesis P(k). . Define the statement P(k + 1) that must be shown. . Show your algebra throughout the proof. Edit View Insert Format Tools Table 12pt \\ Paragraph [ B I U A V Q V T V Q V E V B V B V O YV VEVE DBV VX 0 words > >