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7. [4 marks]. Consider the sequence of numbers vector{b} defined recursively as follows: - Base case: b_{0}=3 . - Recursive case: for n ≥slant 1 , we have b_{n}=2 b_{n-1}+n . Giv

User Lannetta
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Answer and Step-by-step explanation:

The sequence of numbers vector{b} is defined recursively as follows:

- Base case: b_{0} = 3

- Recursive case: For n ≥ 1, we have b_{n} = 2 b_{n-1} + n

To better understand this recursive definition, let's examine how the sequence is generated step by step:

1. Starting with the base case, we have b_{0} = 3.

2. Using the recursive case, we can find the next term in the sequence:

- For n = 1: b_{1} = 2 * b_{0} + 1 = 2 * 3 + 1 = 7

- For n = 2: b_{2} = 2 * b_{1} + 2 = 2 * 7 + 2 = 16

- For n = 3: b_{3} = 2 * b_{2} + 3 = 2 * 16 + 3 = 35

- And so on...

We can continue this process to generate more terms in the sequence by substituting the previous term into the recursive formula.

In summary, the sequence vector{b} is defined recursively, starting with the base case b_{0} = 3, and each subsequent term is obtained by multiplying the previous term by 2 and adding the value of n.

User Maruful
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