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Sequences:
Determine the general term of the following sequences:

A. 3, 7, 11, 15, 19, ...

B. -3, 9, -27, 81, -243, ...

C. [tex]\frac{3}{4} , \frac{5}{7} , \frac{7}{10} , \frac{9}{13} , \frac{11}{16} , ...[/tex]

Respuesta :

mhanifa

Answer:

A.

  • 3, 7, 11, 15, 19, ...

The first term is 3 and the common difference is 4.

The nth term is:

  • aₙ = a₁ + (n - 1)d
  • aₙ = 3 + 4(n - 1) = 4n - 1
  • aₙ = 4n - 1

B.

  • -3, 9, -27, 81, -243, ...

The first term is -3 and common ratio is -3.

The nth term is:

  • aₙ = a₁rⁿ⁻¹
  • aₙ = -3*(-3)ⁿ⁻¹ = (-3)°
  • aₙ = (-3)ⁿ

C.

  • 3/4, 5/7, 7/10, 9/13, 11/16, ...

The numerator and the denominator are both AP.

The numerator:

  • b₁ = 3, d = 2

The nth term is:

  • bₙ = 3 + 2(n - 1) = 2n + 1

The denominator:

  • c₁ = 4, d = 3

The nth term is:

  • cₙ = 4 + 3(n - 1) = 3n + 1

The nth term of the sequence is:

  • aₙ = bₙ/cₙ
  • aₙ = (2n + 1)/(3n + 1)

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