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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.\newline5,6,7,8,…5, 6, 7, 8, \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.\newline5,6,7,8,…5, 6, 7, 8, \ldots\newline_____\_\_\_\_\_
  1. Sequence Analysis: First, let's look at the sequence: 5,6,7,8,…5, 6, 7, 8, \ldots Each term increases by 11 from the previous term. So, the difference between consecutive terms is 11. This is an arithmetic sequence with a common difference of 11.
  2. Arithmetic Sequence Formula: To write an expression for the nth term of an arithmetic sequence, we use the formula: nth term=first term+(n−1)×common difference\text{nth term} = \text{first term} + (n - 1) \times \text{common difference}. Here, the first term is 55 and the common difference is 11.
  3. Expression for nth Term: Plug in the values into the formula: nth term=5+(n−1)×1\text{nth term} = 5 + (n - 1) \times 1. This simplifies to nth term=5+n−1\text{nth term} = 5 + n - 1.
  4. Simplify Expression: Now, simplify the expression: nth term=5+n−1\text{nth term} = 5 + n - 1 turns into nth term=n+4\text{nth term} = n + 4.

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