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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.\newline77,154,231,308,…77, 154, 231, 308, \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.\newline77,154,231,308,…77, 154, 231, 308, \ldots\newlinean=a_n = _____
  1. Sequence Type: We have: \newline77,154,231,308,…77, 154, 231, 308, \ldots \newlineIs the given sequence geometric or arithmetic? \newlineTo determine this, we can look at the differences or ratios between terms.
  2. Calculate Differences: 77,154,231,308,…77, 154, 231, 308, \ldots \newlineCalculate the difference between consecutive terms to see if it is constant.\newlineDifference between second and first term: 154−77=77154 - 77 = 77\newlineDifference between third and second term: 231−154=77231 - 154 = 77\newlineDifference between fourth and third term: 308−231=77308 - 231 = 77\newlineSince the differences are constant, the sequence is arithmetic.
  3. Find a1a_1 and dd: Determine the values of a1a_1 and dd of the sequence.\newlineThe first term, a1=77a_1 = 77\newlineCommon difference, d=77d = 77 (as calculated in the previous step)
  4. Arithmetic Sequence Formula: We have the formula for the nnth term of an arithmetic sequence: an=a1+(n−1)da_n = a_1 + (n-1)d a1=77a_1 = 77 d=77d = 77 Write an expression to describe 77,154,231,308,…77, 154, 231, 308, \ldots an=77+(n−1)×77a_n = 77 + (n-1)\times77
  5. Simplify Expression: Simplify the expression:\newlinean=77+77n−77a_{n} = 77 + 77n - 77\newlinean=77na_{n} = 77n\newlineThis is the expression that describes the sequence.

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