Suppose that Park, . ... Is a sequence defined as follows. fo - 5,f - 16, - 71 1 - 10f _ 2 for every Integer k 2 2 Prove that ( = 3 . 2" + 2 . 5" for each Integer n 2 0. Proof by strong mathematical induction: Let the property Pin) be the equation / = 3 - 2" + 2 - 5". We will show that Pinj is true for every Integer n 2 0. Show that P(0) and P(1) are truc: Select A0) from the choices below. O P(D) - 3 - 2 + 2 - 5 Of - 5 Of -3 - 2+2. 50 Select Al) from the cholers below. Of- 16 O P(1) - 3 - 2' + 2- 51 Or - 3- 21 + 2. 51 OF(1) - PD) and P(1) are true because 3 . 2 + 2 . 5" - 5 and 3 . 2' + 2 - 51 = 16. Show that for every integer k 2 1, If P(I) is true for each integer i from 0 through k, then P(k + 1) is true: Let & be any Integer with A 2 1, and suppose that for every Integer / with 0 S / s k, f - This Is the -Saloct... V . We must show that ( 4 1 Now, by definition of farrar .-.. Apply the inductive hypothesis to f and foo, and complete the proof as a free response. (Submit a file with a maximum size of 1 MB. )Compute go, 91, 94, 93, 94, and 95. 92 95 Make a conjecture about the units digit of 9", where n is a nonnegative Integer. If in is even, the units digit of g" is . If n is odd, the units digit of 9" is Use strong mathematical Induction to prove your conjecture. Submit your proof as a fires response. (Submit a file with a maximum size of 1 ME.] Chonon File No file chosen