14. If the numbers an are defined by a₁ = : 11, a2 = 21, and an = 3an–1 — 2an-2 for n ≥ 3, prove that an = 5 · 2n +1 n≥ 1

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Q: (7) The difference of two odd integers x and y is 4. Prove that x and y are relatively prime.

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A: As per the guideline i am uploading the first two. For the other two kindly resubmit the questions…

Q: Let A = 2 21 -1 1 1 0 3 3 ---B 3 Calculate A¹, and use A to solve Ax

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Q: 14. Give a geometric explanation of why 2π/n 1-2 0 r² do = лr² 2 for any positive real number r and…

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Q: 1. Show for all natural numbers n that (2k – 1) = 1+3+ ...+ (2n – 1) = n². k=1

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Q: is a1 = 2, a2 =3, and an  = 5an–1 – 4an–2 for n > 2 expressed in explicit formula? true or false?

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Q: Let, a1= 3 and for n ≥ 2, an = 2an-1 + 1, express an in terms of n.

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Q: Show that if n is a positive integer, then fo(n) (26(n) $(2n) = if n is odd if n is even.

A: Given- n is a positive integer. To prove- ϕ2n=ϕn     if n is odd2ϕn   if n is even   Result Used-…