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Imran and Aubrey were asked to find an explicit formula for the sequence 14,5,-4,-13,dots, where the first term should be g(1). Imran said the formula is g(n)=14-9(n-1). Aubrey said the formula is g(n)=14-9n. Which one of them is right? Choose 1 answer: (A) Only Imran (B) Only Aubrey (c) Both Imran and Aubrey (D) Neither Imran nor Aubrey

Imran and Aubrey were asked to find an explicit formula for the sequence 14,5,−4,−13,… 14,5,-4,-13, \ldots , where the first term should be g(1) g(1) .\newlineImran said the formula is g(n)=14−9(n−1) g(n)=14-9(n-1) .\newlineAubrey said the formula is g(n)=14−9n g(n)=14-9 n .\newlineWhich one of them is right?\newlineChoose 11 answer:\newline(A) Only Imran\newline(B) Only Aubrey\newline(C) Both Imran and Aubrey\newline(D) Neither Imran nor Aubrey

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Q. Imran and Aubrey were asked to find an explicit formula for the sequence 14,5,−4,−13,… 14,5,-4,-13, \ldots , where the first term should be g(1) g(1) .\newlineImran said the formula is g(n)=14−9(n−1) g(n)=14-9(n-1) .\newlineAubrey said the formula is g(n)=14−9n g(n)=14-9 n .\newlineWhich one of them is right?\newlineChoose 11 answer:\newline(A) Only Imran\newline(B) Only Aubrey\newline(C) Both Imran and Aubrey\newline(D) Neither Imran nor Aubrey
  1. Identify sequence type: Identify the type of sequence. The sequence 14,5,−4,−13,extellipsis14, 5, -4, -13, extellipsis has a constant difference between consecutive terms, which means it is an arithmetic sequence.
  2. Determine common difference: Determine the common difference dd of the sequence. The difference between the first term 1414 and the second term 55 is 5−14=−95 - 14 = -9. This is the common difference.
  3. Use arithmetic sequence formula: Use the arithmetic sequence formula to find the nth term: g(n)=g(1)+(n−1)dg(n) = g(1) + (n-1)d. The first term g(1)g(1) is 1414, and the common difference dd is −9-9.
  4. Substitute values into formula: Substitute the values of g(1)g(1) and dd into the formula. The formula becomes g(n)=14+(n−1)(−9)g(n) = 14 + (n-1)(-9), which simplifies to g(n)=14−9(n−1)g(n) = 14 - 9(n-1).
  5. Compare with provided formulas: Compare the derived formula with the formulas provided by Imran and Aubrey. Imran's formula is g(n)=14−9(n−1)g(n) = 14 - 9(n-1), which matches the formula we derived. Aubrey's formula is g(n)=14−9ng(n) = 14 - 9n, which does not match because it does not account for the first term being 1414 when n=1n=1.

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