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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.\newline4,5,6,7,…4, 5, 6, 7, \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.\newline4,5,6,7,…4, 5, 6, 7, \ldots\newlinean=a_n = _____
  1. Identify Sequence Type: Identify the type of sequence.\newlineThe sequence is 4,5,6,7,…4, 5, 6, 7, \ldots Each term increases by 11 from the previous term, which indicates that this is an arithmetic sequence.
  2. Find First Term and Difference: Determine the first term (a1a_1) and the common difference (dd). The first term a1a_1 is 44. The common difference dd can be found by subtracting the first term from the second term: d=5−4=1d = 5 - 4 = 1.
  3. Write nth Term Formula: Write the formula for the nth term of an arithmetic sequence.\newlineThe nth term ana_n of an arithmetic sequence is given by the formula an=a1+(n−1)da_n = a_1 + (n - 1)d.
  4. Substitute Values: Substitute the values of a1a_{1} and dd into the formula.an=4+(n−1)×1.a_{n} = 4 + (n - 1)\times1.
  5. Simplify Expression: Simplify the expression.\newlinean=4+n−1a_n = 4 + n - 1.\newlinean=n+3a_n = n + 3.

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