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3 years ago

Is the sequence 5,9,15———-an arithmetic?

Mathematics

2 answers:

Mademuasel [1]3 years ago

6 0

Answer:

No, the given sequence is not arithmetic.

Step-by-step explanation:

The given sequence is

$5,9,15,....$

The first term is 5.

A sequence is an arithmetic, if the difference between any two consecutive terms are same.

The difference between terms are

$d_1=9-5=4$

$d_2=15-9=6$

$d_1\neq d_2$

Since the difference between consecutive terms are not same, therefore given sequence is not arithmetic.

Veseljchak [2.6K]3 years ago

4 0

Answer:

5, 9, 15,....is not an arithmetic sequence.

Step-by-step explanation:

Arithmetic sequence is a sequence in which difference between the consecutive terms is constant.

Example: 0 , 5, 10, 15, 20 is an arithmetic sequence with common difference of 5 between the terms.

Consider the given sequence,

5, 9, 15,....

Here, $a_1=5\\\\a_2=9\\\\a_3=15$

We first find the difference between the terms,

$a_2-a_1=9-5=4$

$a_3-a_2=15-9=6$

Since the difference is not constant .

So,it is not an arithmetic sequence.

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2 years ago

Exercise 2.4.2: Proving statements about rational numbers with direct proofs. About Prove each of the following statements using

IgorLugansk [536]

Answer:

See Explanation

Step-by-step explanation:

(a) Proof: Product of two rational numbers

Using direct proofs.

Let the two rational numbers be A and B.

Such that:

$A = \frac{1}{2}$

$B = \frac{2}{3}$

The product:

$A * B = \frac{1}{2} * \frac{2}{3}$

$A * B = \frac{1}{1} * \frac{1}{3}$

$A * B = 1 * \frac{1}{3}$

$A * B = \frac{1}{3}$

Proved, because 1/3 is rational

(b) Proof: Quotient of a rational number and a non-zero rational number

Using direct proofs.

Let the two rational numbers be A and B.

Such that:

$A = \frac{1}{2}$

$B = \frac{2}{3}$

The quotient:

$A / B = \frac{1}{2} / \frac{2}{3}$

Express as product

$A / B = \frac{1}{2} / \frac{3}{2}$

$A / B = \frac{1*3}{2*2}$

$A / B = \frac{3}{4}$

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(c) x + y is rational (missing from the question)

Using direct proofs.

Let x and y be

Such that:

$x = \frac{1}{2}$

$y = \frac{2}{3}$

The sum:

$x + y = \frac{1}{2} + \frac{2}{3}$

Take LCM

$x + y = \frac{3+4}{6}$

$x + y = \frac{7}{6}$

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<em>The above proof works for all values of A, B, x and y; as long as they are rational values</em>

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3 years ago

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bixtya [17]

Answer:

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Step-by-step explanation:

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2 years ago

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Answer:

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