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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.\newline73,146,219,292,…73, 146, 219, 292, \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.\newline73,146,219,292,…73, 146, 219, 292, \ldots\newlinean=a_n = _____
  1. Given Sequence Analysis: We have: \newline73,146,219,292,…73, 146, 219, 292, \ldots \newlineIs the given sequence geometric or arithmetic? \newlineTo determine this, we look at the differences between consecutive terms.
  2. Calculate Common Difference: Calculate the common difference between consecutive terms:\newline146−73=73146 - 73 = 73\newline219−146=73219 - 146 = 73\newline292−219=73292 - 219 = 73\newlineSince the difference is constant, the sequence is arithmetic.
  3. Determine a1a_1 and dd: Determine the values of a1a_1 and dd of the sequence.\newlineThe first term, a1=73a_1 = 73\newlineCommon difference, d=146−73=73d = 146 - 73 = 73
  4. Arithmetic Sequence Formula: Write the formula for the nth term of an arithmetic sequence:\newlinean=a1+(n−1)da_n = a_1 + (n-1)d\newlineSubstitute the values of a1a_1 and dd into the formula:\newlinean=73+(n−1)×73a_n = 73 + (n-1)\times73
  5. Simplify Expression: Simplify the expression:\newlinean=73+73n−73a_{n} = 73 + 73n - 73\newlinean=73na_{n} = 73n

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