Respuesta :

mhanifa

Answer:

  • The 27th term is 22

Step-by-step explanation:

Let the first term is a and common difference is d.

The nth term is:

  • aₙ = a + (n - 1)d

We have:

  • a₆ = 15
  • a₉ = 16

The difference of these terms is:

  • (a + 8d) - (a + 5d) = 16 - 15
  • 3d = 1
  • d = 1/3

Then the first term is:

  • a + 5*1/3 = 15
  • a = 15 - 5/3 = 13 1/3

The nth term equation is:

  • aₙ = 13 1/3 + 1/3(n - 1) = 1/3n + 13

If the nth term is 22, find n:

  • 1/3n + 13 = 22
  • 1/3n = 22 - 13
  • 1/3n = 9
  • n = 9*3
  • n = 27

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