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eimsori [14]
3 years ago
12

Write a recursive formula for the sequence -2,4,-8, 16, ...

Mathematics
1 answer:
VARVARA [1.3K]3 years ago
5 0

Answer:

a_1 = -2;~a_n = -2a_{n - 1}, ~n \ge 2

Step-by-step explanation:

The first number in the sequence, a_1, is -2.

Each number after that is the previous number multiplied by -2.

a_1 = -2

a_2 = a_1 \times (-2) = -2 \times (-2) = 4

a_3 = a_2 \times (-2) = 4 \times (-2) = -8

etc.

a_n = -2a_{n - 1}

We start by stating that a_1 = -2.

Now we need to show that for all n greater than or equal to 2, each number in the sequence is the previous number multiplied by -2.

a_n = -2a_{n - 1}

Answer:

a_1 = -2;~a_n = -2a_{n - 1}, ~n \ge 2

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Using it's concepts, the average speed and the average velocity are given as follows:

  • Average speed: 40 miles per hour.
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<h3>Average speed</h3>

The average speed is given by the quotient between the total distance traveled and the time taken, that is:

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In this problem, the total distance is of 60 miles(30 miles west + 30 miles south), in a time of 1.5 hours(1 hour west and 0.5 hours south), hence the average speed is given as follows:

Average speed = 60/1.5 = 40 miles per hour.

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The average velocity is given by the quotient between the displacement and the time taken, that is:

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makvit [3.9K]

Answer:

A <u>rational number</u> is a number that can be expressed as a fraction (the ratio of two integers).  

<u>Integer</u>:  A whole number that can be positive, negative, or zero.

To calculate if each radical can be expressed as a rational number, convert the decimals into rational numbers, then simplify:

\sqrt{121}=\sqrt{11^2}=11=\dfrac{11}{1} \quad \leftarrow \textsf{rational}

\sqrt{12.1}=\sqrt{\dfrac{1210}{100}}=\dfrac{\sqrt{1210}}{\sqrt{100}}=\dfrac{\sqrt{121\cdot 10}}{10}=\dfrac{\sqrt{121}\sqrt{10}}{10}=\dfrac{11\sqrt{10}}{10} \leftarrow \textsf{not rational}

\sqrt{1.21}=\sqrt{\dfrac{121}{100}}=\dfrac{\sqrt{121}}{\sqrt{100}}=\dfrac{\sqrt{11^2}}{\sqrt{10^2}}=\dfrac{11}{10} \leftarrow \textsf{rational}

\sqrt{0.0121}=\sqrt{\dfrac{121}{10000}}=\dfrac{\sqrt{121}}{\sqrt{10000}}=\dfrac{\sqrt{11^2}}{\sqrt{100^2}}=\dfrac{11}{100} \leftarrow \textsf{rational}

Therefore, \sf \sqrt{12.1} is not a rational number.

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