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Leokris [45]
3 years ago
11

Identify the first five terms of the sequence in which a1 = 5 and an = 2an−1−3 for n ≥ 2.

Mathematics
1 answer:
ziro4ka [17]3 years ago
3 0

Answer:

5, 7, 11, 19, 35

Step-by-step explanation:

Using the recursive formula and a₁ = 5 , then

a₂ = 2a₁ - 3 = (2 × 5) - 3 = 10 - 3 = 7

a₃ = 2a₂ - 3 = (2 × 7) - 3 = 14 - 3 = 11

a₄ = 2a₃ - 3 = (2 × 11) - 3 = 22 - 3 = 19

a₅ = 2a₄ - 3 = (2 × 19) - 3 = 38 - 3 = 35

Thus the first 5 terms are

5, 7, 11, 19, 35

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pentagon [3]
First, multiply the first equation by 2.

That turns the first equation into:

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That way it can easily be added to the second equation:

6x - 2y = 16
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7x = 21
==========

As you can see, the y disappeared, which was the objective of this operation.

Now the equations can be solved easily:

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Insert x=3 in the original equation:

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Step-by-step explanation:

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