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Given the sequence 4, 0.2, -3.6, -7.4, -11.2 Determine its nᵗʰ term

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Final answer:

The nᵗʰ term of the given arithmetic sequence is 7.8 - 3.8n, which is found by identifying the common difference and applying the formula for the nth term of an arithmetic sequence, Tₙ = a₁ + (n - 1)d.

Step-by-step explanation:

To determine the nᵗʰ term of the given sequence 4, 0.2, -3.6, -7.4, -11.2, we need to identify the pattern or rule that the sequence follows. This sequence is an arithmetic sequence because each term is found by adding a constant number to the previous term. In this case, that constant number is the common difference.

To find the common difference, we subtract any term from the term that follows it:

  1. 0.2 - 4 = -3.8
  2. -3.6 - 0.2 = -3.8
  3. -7.4 - (-3.6) = -3.8
  4. -11.2 - (-7.4) = -3.8

Since the common difference is -3.8, we can express the nᵗʰ term, or Tₙ, of an arithmetic sequence with the formula:

Tₙ = a₁ + (n - 1)d

Where:

  • a₁ is the first term of the sequence, which is 4.
  • d is the common difference, which is -3.8.
  • n is the term number.

We can now find the nᵗʰ term formula:

Tₙ = 4 + (n - 1)(-3.8)

Tₙ = 4 - 3.8n + 3.8

Tₙ = 7.8 - 3.8n

Thus, the nᵗʰ term of the sequence is 7.8 - 3.8n.

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