Question: Consider a sequence 5, 11, 19, 29, 41, 55, ... Assume a 1 = 5. (a) Find a closed formula for a n , the

Consider a sequence 5, 11, 19, 29, 41, 55, ... Assume a₁ = 5.

(a) Find a closed formula for a_n , the n^th term of the sequence, by writing each term as a sum of a sequence. Hint: first find a₀ , but ignore it when collapsing the sum.

(b) Find a closed formula again, this time using either polynomial fitting or the root characteristics technique.

(c) Find a closed formula once again, this time by recognizing the sequence as a modification to some well-known sequence(s). Explain

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