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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.\newline43,44,45,46,…43, 44, 45, 46, \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.\newline43,44,45,46,…43, 44, 45, 46, \ldots\newlinean=a_n = _____
  1. Identify Sequence Type: We have the sequence: 43,44,45,46,…43, 44, 45, 46, \ldots 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=43a_1 = 43 \newlineThe common difference, d=44−43=1d = 44 - 43 = 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=43a_1 = 43 and d=1d = 1 into the formula to find the expression for ana_n.
  4. Write Sequence Expression: Write the expression for the sequence: \newlinean=43+(n−1)×1a_{n} = 43 + (n-1)\times 1 \newlineSimplify the expression: \newlinean=43+n−1a_{n} = 43 + n - 1 \newlinean=n+42a_{n} = n + 42

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