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Let {an }n>o be a sequence defined by a = n² + 2n − 3 for every n>0 a) Find the firsts 3 (elements) elements of the sequence. b) Show that the sequence satisfies the recurrence relation An = 2an-1 − An-2 +2 for every n ≥ 2. c) Find a closed formula for the first difference of the sequence {an}n>0² i.e., Δαπ = an+1-an for every n > 0.

Let {an }n>o be a sequence defined by a = n² + 2n − 3 for every n>0 a) Find the firsts 3 (elements) elements of the sequence. b) Show that the sequence satisfies the recurrence relation An = 2an-1 − An-2 +2 for every n ≥ 2. c) Find a closed formula for the first difference of the sequence {an}n>0² i.e., Δαπ = an+1-an for every n > 0.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.1: Infinite Sequences And Summation Notation
Problem 74E
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Let {an}nzo be a sequence defined by an = n² + 2n - 3 for every n ≥ 0 a) Find the firsts 3 (elements) elements of the sequence. b) Show that the sequence satisfies the recurrence relation An = 2an-1-an-2 +2 for every n > 2. c) Find a closed formula for the first difference of the sequence {an}n>0. i.e., Δαπ = an+1-an for every n > 0.
Transcribed Image Text:Let {an}nzo be a sequence defined by an = n² + 2n - 3 for every n ≥ 0 a) Find the firsts 3 (elements) elements of the sequence. b) Show that the sequence satisfies the recurrence relation An = 2an-1-an-2 +2 for every n > 2. c) Find a closed formula for the first difference of the sequence {an}n>0. i.e., Δαπ = an+1-an for every n > 0.
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