Suppose that f0, f1, f2, is a sequence defined as follows. f0 = 5, f1 = 16, fk = 7fk − 1 − 10fk − 2 for every integer k

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Suppose that f0, f1, f2, is a sequence defined as follows. f0 =5, f1 = 16, fk = 7fk − 1 − 10fk − 2 for every integer k ≥ 2 Provethat fn = 3 · 2n + 2 · 5n for each integer n ≥ 0. Proof by strongmathematical induction: Let the property P(n) be the equation fn =3 · 2n + 2 · 5n. We will show that P(n) is true for every integer n≥ 0. Show that P(0) and P(1) are true: Select P(0) from the choicesbelow. f0 = 3 · 20 + 2 · 50 f0 = 5 P(0) = f0 P(0) = 3 · 20 + 2 · 50Select P(1) from the choices below. f1 = 3 · 21 + 2 · 51 P(1) = f1P(1) = 3 · 21 + 2 · 51 f1 = 16 P(0) and P(1) are true because 3 ·20 + 2 · 50 = 5 and 3 · 21 + 2 · 51 = 16. Show that for everyinteger k ≥ 1, if P(i) is true for each integer i from 0 through k,then P(k + 1) is true: Let k be any integer with k ≥ 1, and supposethat for every integer i with 0 ≤ i ≤ k, fi = . This is the---Select--- . We must show that fk + 1 = . Now, by definition off0, f1, f2, , fk + 1 = .

Suppose That F0 F1 F2 Is A Sequence Defined As Follows F0 5 F1 16 Fk 7fk 1 10fk 2 For Every Integer K 1 (68.63 KiB) Viewed 34 times

Suppose that for f₁ f2 is a sequence defined as follows. fo = 5, f₁ = 16, fk = 7fk-1-10fk-2 for every integer k ≥ 2 Prove that f = 3.2" +2.5" for each integer n ≥ 0. Proof by strong mathematical induction: Let the property P(n) be the equation f = 3.2" +2.5". We will show that P(n) is true for every integer n ≥ 0. Show that P(0) and P(1) are true: Select P(0) from the choices below. fo=3.20 +2.5⁰ O fo = 5 O P(0) = fo ⒸP(0) = 3.20 +2.5⁰ Select P(1) from the choices below. Of₁3.2¹ +2.5¹ O P(1) = f₁ OP(1) - 3.2¹ +2.5¹ O f₁ = 16 P(0) and P(1) are true because 320 +2.50 = 5 and 3.2¹ +2.5¹ = 16. Show that for every integer k ≥ 1, if P(i) is true for each integer i from 0 through k, then P(k+ 1) is true: Let k be any integer with k ≥ 1, and suppose that for every integer i with 0 ≤isk, f₁ = . This the ---Select--- Now, by definition of for f₁ f₂. fk + 1 = Apply the inductive hypothesis to f and f and complete the proof as a free response. (Submit a file with a maximum size of 1 MB.) . We must show that fk + 1 =