= 1, a2 = 4, a3 = 9, and for n ≥ 4, an = B. A sequence (an)n≥1 is defined recursively by a₁ = an-1 + an-2-an-3 +4. For all n € N, state a formula for an, and prove the formula using induction.

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A:

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A: Given:-               Let T = {0,1,2}. A string x ∈ T" is said to be balanced if the sum of the…

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A:

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A: The correct answer is given below:-

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Q: 2 proofs of binomial identities applied to Pell-Lucas numbers.

A: The Pell-Lucas numbers are a sequence of integers defined by the recurrence relation: P(n) = 2P(n-1)…

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A:

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Q: none of these answers were correct

A: Note:The previous solution is also correct and given by using an inverse matrix method.I have given…

Q: Prove: For all integers n, if n is odd then n is odd.

A: Given below the detailed solution

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A: To express the complex number z=-6-6j, in the polar form z=rcos θ+j sin θ, where -π<θ≤π.

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A: Given statement: Sum of digits of any number (x) in any base b is divisible by b-1. To prove: The…

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A:

Q: 1. Use the fractal pattern to write the recursive and explicit formula. a. What is the pattern? List…

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Q: 9 – i 3 + 9i If A = find A*. 7+ 5i -4 + 8i ( ) ? ? ? ? A*

A:

Q: did not acccept

A: We are asked to evaluate the integral

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Q: Solve by mathematical induction For all integersn> 3, 4(4" – 16) 4 + 4* +4 + .. ……+4" =

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Q: - -

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A:

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Q: 6479x + 1053y = 4.

A: Calculating GCD(6479,1053) gives: 1053 = 0*6479 + 1053 6479 = 6*1053 + 161 1053 = 6*161 + 87 161 =…