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The third term of an arithmetic sequence is -14 And the fifth term is -30. Determine the nᵗʰ term of the sequence

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Final answer:

To find the nᵗʰ term of the given arithmetic sequence, we first calculated the common difference, then found the first term, and formulated the nᵗʰ term: Tₙ = 10 - 8n.

Step-by-step explanation:

Arithmetic sequence problems involve finding a specific term within a sequence where the difference between consecutive terms is constant. In this case, we are given the third term (-14) and the fifth term (-30) of an arithmetic sequence and must determine the nth term of the sequence.

To find the nth term, we will use the formula for an arithmetic sequence:
Tn = a + (n-1)d, where Tn is the nth term, a is the first term, and d is the common difference.

Step 1: Find the common difference (d) using the given terms. Since the sequence progresses from the third to the fifth term, there are two steps, so:

  • (-30) - (-14) = -16
  • d = -16 / 2 = -8

Step 2: Find the first term (a). We can use the third term for this:

  • -14 = a + 2(-8)
  • -14 = a - 16
  • a = 2

Step 3: Write the formula for the nth term:

Tn = 2 + (n-1)(-8)

Step 4: Simplify the formula:

Tn = 2 - 8n + 8

Tn = 10 - 8n

The nth term of the sequence is 10 - 8n.

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