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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.\newline57,114,171,228,…57, 114, 171, 228, \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.\newline57,114,171,228,…57, 114, 171, 228, \ldots\newlinean=a_n = _____
  1. Identify Sequence Type: We have: \newline57,114,171,228,…57, 114, 171, 228, \ldots \newlineIs the given sequence geometric or arithmetic? \newlineTo determine this, we can look at the differences between consecutive terms.
  2. Calculate Differences: Calculate the difference between the second term and the first term: \newline114−57=57114 - 57 = 57\newlineNow, calculate the difference between the third term and the second term: \newline171−114=57171 - 114 = 57\newlineSince the differences are the same, the given sequence is arithmetic.
  3. Find a1a_1 and dd: Determine the values of a1a_1 and dd of the sequence. \newlineThe first term, a1=57a_1 = 57 \newlineCommon difference, d=114−57=57d = 114 - 57 = 57
  4. Use nth Term Formula: We have 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=57+(n−1)×57a_n = 57 + (n-1)\times57
  5. Simplify Expression: Simplify the expression: \newlinean=57+57n−57a_{n} = 57 + 57n - 57\newlinean=57na_{n} = 57n

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