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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.\newline84,168,252,336,…84, 168, 252, 336, \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.\newline84,168,252,336,…84, 168, 252, 336, \ldots\newlinean=a_n = _____
  1. Given Sequence Analysis: We have: \newline84,168,252,336,…84, 168, 252, 336, \ldots \newlineIs the given sequence geometric or arithmetic? \newlineTo determine this, we can look at the differences or ratios between terms.
  2. Calculate Constant Difference: Calculate the difference between consecutive terms to see if it is constant: 168−84=84168 - 84 = 84 252−168=84252 - 168 = 84 336−252=84336 - 252 = 84 Since the difference is constant, the sequence is arithmetic.
  3. Find a1a_1 and dd: Determine the values of a1a_1 and dd for the sequence.\newlineThe first term, a1=84a_1 = 84\newlineCommon difference, d=168−84=84d = 168 - 84 = 84
  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=84+(n−1)×84a_n = 84 + (n-1)\times84
  5. Simplify Expression: Simplify the expression:\newlinean=84+84n−84a_{n} = 84 + 84n - 84\newlinean=84na_{n} = 84n

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