Respuesta :

Ashraf82

Answer:

Arithmetic sequence:  [tex]a_{n}=a_{1}+(n-1)d[/tex]

Geometric sequence: [tex]a_{n}=a_{1}(r)^{n-1}[/tex]

Step-by-step explanation:

The arithmetic sequence: is the sequence whos terms increased or decreased by a constant amount.

Examples:

  • 4, 7, 10, 13, 16, ........................ (increased by 3)
  • 25, 20, 15, 10, ......................... (Decreased by 5)

The explicit formula for the nth term of the arithmetic sequence is:

  • [tex]a_{n}=a_{1}+(n-1)d[/tex]
  • [tex]a_{1}[/tex] is the first term
  • d is the constant difference between each two consecutive terms
  • n is the position of the number in the sequence

The geometric sequence: is the sequence whos consecutive terms have a constant ratio

Examples:

  • 1, 2, 4, 8, 16, ........................ (Multiplying by 2)
  • 625, 125, 25, 5, ......................... (Dividing by 5)

The explicit formula for the nth term of the geometric sequence is:

  • [tex]a_{n}=a_{1}(r)^{n-1}[/tex]
  • [tex]a_{1}[/tex] is the first term
  • r is the constant ratio between each two consecutive terms
  • n is the position of the number in the sequence

* Arithmetic sequence          →→→→→→   Geometric sequence

 Has a constant difference    →→→→→→    Has a constant ratio

 [tex]a_{n}=a_{1}+(n-1)d[/tex]                  →→→→→→    [tex]a_{n}=a_{1}(r)^{n-1}[/tex]

 [tex]d=a_{n}-a_{n-1}[/tex]                          →→→→→→    [tex]r=\frac{a_{n}}{a_{n-1} }[/tex]

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