Find the solution to the recurrence relation and prove the correctness of your solution using mathematical induction. a_n=a_{n-1}+3, n >= 1; a_0=1

Emmanuel Pace 2022-07-18 Answered
Recurrence relations Discrete Math
Instructions say: Find the solution to the recurrence relation and prove the correctness of your solution using mathematical induction.
a n = a n 1 + 3 , n 1 ; a 0 = 1
Please help I am completely confused, I've read the textbook section on mathematical induction and I'm so confused please be as descriptive in your explanations as possible.
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Answers (1)

Tristan Pittman
Answered 2022-07-19 Author has 14 answers
Step 1
As a n a n 1 = 3 which is independent of n
it is an Arithmetic Series with common difference = 3
So, a n = a 0 + n 3
Step 2
For the inductive proof, let a n = a 0 + n 3 holds true for n = m
i.e., a m = a 0 + m 3
a m + 1 = a m + 3 =
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