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Given the sequence 17, -24, -65, -106, -147 Determine its nᵗʰ term

User Iskander
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1 Answer

3 votes

Final answer:

The nth term of the sequence is found using the arithmetic sequence formula an = a1 + (n - 1)d. For the sequence 17, -24, -65, -106, -147, the nth term is an = 58 - 41n.

Step-by-step explanation:

To find the nth term of the given sequence 17, -24, -65, -106, -147, let's first determine the pattern of the sequence.

If we look at the differences between the terms:

  • -24 - 17 = -41
  • -65 - (-24) = -41
  • -106 - (-65) = -41
  • -147 - (-106) = -41

we see that the difference is constant and equal to -41. This indicates that the sequence is an arithmetic sequence with a common difference of -41.

The first term (a1) in the sequence is 17, and with the common difference (d) being -41, we can use the formula for the nth term of an arithmetic sequence:

an = a1 + (n - 1)d

Plugging in the values:

an = 17 + (n - 1)(-41)

Simplify to find the nth term:

an = 17 - 41n + 41

an = 58 - 41n

So, the nth term of the sequence is an = 58 - 41n.

User Bruce Patin
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