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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.\newline9,10,11,12,…9, 10, 11, 12, \ldots\newline__\_\_

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Write variable expressions for arithmetic sequencesright chevron icon

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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.\newline9,10,11,12,…9, 10, 11, 12, \ldots\newline__\_\_
  1. Identify Pattern: Step 11: Identify the pattern in the sequence.\newlineThe sequence starts at 99 and each subsequent term increases by 11.\newlineReasoning: The first term is 99, the second term is 1010 (9+19+1), the third term is 1111 (10+110+1), and so on.\newlineCalculation: 9,10,11,12,…9, 10, 11, 12, \ldots
  2. Formulate Expression: Step 22: Formulate the expression using nn.\newlineSince the sequence starts at 99 and increases by 11 for each subsequent term, the nnth term can be expressed as the first term plus (n−1)(n-1) times the common difference (which is 11).\newlineReasoning: The nnth term = first term + (n−1)(n-1) * common difference.\newlineCalculation: nnth term = 9+(n−1)∗19 + (n-1) * 1
  3. Simplify Expression: Step 33: Simplify the expression.\newlineSimplify the expression derived in Step 22.\newlineReasoning: Simplify 9+(n−1)×19 + (n-1) \times 1.\newlineCalculation: nth term = 9+n−1=8+n9 + n - 1 = 8 + n.

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