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Write an expression to describe the sequence below. Use nn to represent the position of a term in the sequence, where n=1n = 1 for the first term. –8–8, –16–16, –24–24, –32–32, ...

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Q. Write an expression to describe the sequence below. Use nn to represent the position of a term in the sequence, where n=1n = 1 for the first term. –8–8, –16–16, –24–24, –32–32, ...
  1. Determine Sequence Pattern: We need to determine the pattern of the sequence. The sequence is −8,−16,−24,−32,…-8, -16, -24, -32, \ldots, and we can see that each term is 88 less than the previous term. This indicates that the sequence is arithmetic, with a common difference of −8-8.
  2. Write Expression for nth Term: To write an expression for the nth term of an arithmetic sequence, we use the formula: an=a1+(n−1)da_n = a_1 + (n - 1)d, where ana_n is the nth term, a1a_1 is the first term, and dd is the common difference.
  3. Calculate with Given Values: In this sequence, a1=−8a_1 = -8 (the first term) and d=−8d = -8 (the common difference). Plugging these values into the formula gives us: an=−8+(n−1)(−8)a_n = -8 + (n - 1)(-8).
  4. Simplify Expression: Simplify the expression: an=−8−8(n−1)a_n = -8 - 8(n - 1). Distribute the −8-8 inside the parentheses: an=−8−8n+8a_n = -8 - 8n + 8.
  5. Combine Like Terms: Combine like terms: an=−8na_n = -8n. The +8+8 and −8-8 cancel each other out.

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