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3 years ago

Write the first five terms of the sequence defined by the recursive formula an=2*(an-1)+3 with a1=-2

Mathematics

1 answer:

Tasya [4]3 years ago

5 0

Answer:

<u>The first five terms of the sequence are 5, 7, 9, 11 and 13.</u>

Step-by-step explanation:

The first five terms of the sequence are:

a₁ = 2 * (2 - 1) + 3 = 2 * 1 + 3 = 2 + 3 = 5

a₂ = 2 * (3 - 1) + 3 = 2 * 2 + 3 = 4 + 3 = 7

a₃ = 2 * (4 - 1) + 3 = 2 * 3 + 3 = 6 + 3 = 9

a₄ = 2 * (5 - 1) + 3 = 2 * 4 + 3 = 8 + 3 = 11

a₅ = 2 * (6 - 1) + 3 = 2 * 5 + 3 = 10 + 3 = 13

<u>The first five terms of the sequence are 5, 7, 9, 11 and 13.</u>

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Answer:

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Explanation:

Given f(n) and g(n) defined below:

$\begin{gathered} f\mleft(n\mright)=n^2-3 \\ g\mleft(n\mright)=4n-1 \end{gathered}$

First, we evaluate g(1):

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Therefore:

$\begin{gathered} f\mleft(g(1)\mright)=f\mleft(3\mright) \\ f\mleft(3\mright)=3^2-3 \\ =9-3 \\ =6 \end{gathered}$

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alexandr1967 [171]

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