1. Define a sequence a1, a2, a3, ... by aj = = 1, an = 3an-1 + 4 for n> 2. Give a proof by induction that an 3" – 2 for every n e N.

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.2: Mathematical Induction
Problem 54E: Given the recursively defined sequence , and , use complete induction to prove that for all...
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1. Define a sequence a1, a2, a3, ... by
aj = 1,
an = 3an-1 + 4 for n> 2.
Give a proof by induction that an = 3" – 2 for every n e N.
Transcribed Image Text:1. Define a sequence a1, a2, a3, ... by aj = 1, an = 3an-1 + 4 for n> 2. Give a proof by induction that an = 3" – 2 for every n e N.
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