Respuesta :

mhanifa

Answer:

  • T(n) = 3n² - 4
  • -189 doesn't belong

Step-by-step explanation:

Given sequence:

  • -1, 8, 23, 44, 71

The first differences:

  • 9, 15, 21, 27

The second differences:

  • 6, 6, 6

If the sequence is T(n) = an² + bn + c, we have:

  • 2a = 6 ⇒ a = 3

Using the first and second differences work out  the value of zero term:

  • 9 - 6 = 3
  • -1 - 3 = -4

This gives us c = - 4

Now we have:

  • T(n) = 3n² + bn - 4

The first term is T(1) = -1, substitute n = 1 and find the value of b:

  • 3(1²) + b*1 - 4 = - 1
  • 3 + b - 4 = - 1
  • b = 0

The nth term is:

  • T(n) = 3n² - 4

Now lets find if -189 belongs to this sequence:

  • - 189 = 3n² - 4
  • 3n² = - 185

The left side is positive and the right side is negative so the answer is also negative

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