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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.\newline66,67,68,69,…66, 67, 68, 69, \ldots\newlinean=a_n = _____

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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.\newline66,67,68,69,…66, 67, 68, 69, \ldots\newlinean=a_n = _____
  1. Sequence Type: We have the sequence: 66,67,68,69,ext...66, 67, 68, 69, ext{...} Is the given sequence geometric or arithmetic? Since there is a constant difference between consecutive terms, the given sequence is arithmetic.
  2. Find a1a_1 and dd: Determine the values of a1a_1 (the first term) and dd (the common difference) of the sequence. \newlineThe first term, a1=66a_1 = 66 \newlineThe common difference, d=67−66=1d = 67 - 66 = 1
  3. Use nth term formula: Use the formula for the nth term of an arithmetic sequence: \newlinean=a1+(n−1)da_n = a_1 + (n-1)d \newlineSubstitute a1=66a_1 = 66 and d=1d = 1 into the formula.\newlinean=66+(n−1)×1a_n = 66 + (n-1)\times1
  4. Simplify Expression: Simplify the expression:\newlinean=66+n−1a_{n} = 66 + n - 1 \newlinean=n+65a_{n} = n + 65

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