Consider the following sequence defined recursively: aj = 5, a2 = 8, an+1 = 2an – an-1 + 2, n > 2. Prove that an = n² + 4 for all n E N.
Consider the following sequence defined recursively: aj = 5, a2 = 8, an+1 = 2an – an-1 + 2, n > 2. Prove that an = n² + 4 for all n E N.
Chapter9: Sequences, Probability And Counting Theory
Section9.1: Sequences And Their Notations
Problem 67SE: Consider the sequence defined by an=68n. Is an=421 a term in the sequence? Verify the result.
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![Consider the following sequence defined recursively:
а1 %3D 5, а2 — 8, аn+1 —
: 2ат — ап-1 + 2, п > 2.
Prove that an = n² +4 for all n E N.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4ede9181-eb30-4df7-ba05-68b0bbb5b793%2Fd35f3389-63c9-4ff8-9ac3-483cff758e3f%2Fzbco0r_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the following sequence defined recursively:
а1 %3D 5, а2 — 8, аn+1 —
: 2ат — ап-1 + 2, п > 2.
Prove that an = n² +4 for all n E N.
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