The first 4 terms of the sequence a1-2- an-2 an-1-1 for n - 2 are

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Number Patterns and Sequences

The first 4 t...

Question

The first 4 terms of the sequence a₁ = 2, a_n= 2a_n-1 + 1 for n ≥ 2 are

2, 6, 13, 27

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2, 6, 11, 24

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2, 5, 12, 37

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2, 5, 11, 23

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Solution

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a_{1} = 2, a_{2} = 3 + a_{1}

a_{n} = 2 a_{n - 1} + 5

n > 2

a_{1} = 3, a_{n} = 3 a_{n - 1} + 2

n > 1

a_{1} = a_{2} = a_{3} = 1

a_{n} = a_{n - 1} + a_{n - 2}

n > 3

Find the first four terms of the sequence defined by $a_{1} = 3$ and $a_{n} = 3 a_{n - 1} + 2$ , for all n > 1.

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