Respuesta :

A sequence is a series of numbers  in which there is a mathematical formula  which calculates the next number in the series.

Arithmetic sequence:-  2, 5, 8, 11, 14 ..  The next term is obtained by adding 3.

Geometric sequence:   2, 6, 18, 54 ...     The next term is obtained by multiplying by 3.

A sequence is an arrangement of of numbers in a particular order.

Example of arithmetic sequence : 3, 5, 7, 9, 11

Example of geometric sequence: 4, 8, 16, 32, 64

What is sequence?

"It is an arrangement of a set of numbers in a particular order followed by some rule. "

What is an arithmetic sequence?

"If the difference between consecutive terms of the sequence is constant then the sequence is an arithmetic sequence."

What is geometric sequence?

"If the ratio between consecutive terms of the sequence is constant then the sequence is geometric sequence."

For given question,

A sequence is an arrangement of of numbers in a particular order.

Consider a sequence 3, 5, 7, 9, 11

If take the difference between consecutive terms of above sequence,

5 - 3 = 2

7 - 5 = 2

9 - 7 = 2

11 - 9 = 2

This means, the difference between consecutive terms is constant.

So, the sequence 3, 5, 7, 9, 11 is an arithmetic sequence.

Consider a sequence 4, 8, 16, 32, 64

If take the ratio between consecutive terms of above sequence,

[tex]\frac{8}{4} =2\\\\\frac{16}{8}=2\\\\ \frac{32}{16}=2\\\\\frac{64}{32}=2[/tex]

This means, the ratio between consecutive terms is constant.

So, the sequence 4, 8, 16, 32, 64 is a geometric sequence.

Therefore, a sequence is an arrangement of of numbers in a particular order.

Example of arithmetic sequence : 3, 5, 7, 9, 11

Example of geometric sequence: 4, 8, 16, 32, 64

Learn more about sequence here:

https://brainly.com/question/19819044

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