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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 type of sequence: Identify the type of sequence. The sequence 14,5,−4,−13,ext...14, 5, -4, -13, ext{...} has a constant difference between terms, which makes it 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. Here, g(1)g(1) is the first term, which is 1414, and dd is the common difference, which we found to be −9-9.
  4. Substitute values into formula: Substitute the known values into the formula to get Imran's proposed formula: g(n)=14+(n−1)(−9)g(n) = 14 + (n-1)(-9). Simplify the formula to get g(n)=14−9(n−1)g(n) = 14 - 9(n-1).
  5. Check Imran's formula: Check Imran's formula by plugging in n=2n=2 to see if it gives the second term of the sequence: g(2)=14−9(2−1)=14−9=5g(2) = 14 - 9(2-1) = 14 - 9 = 5. This matches the second term of the sequence, so Imran's formula seems correct so far.
  6. Check Aubrey's formula: Now, check Aubrey's formula by plugging in n=1n=1 to see if it gives the first term of the sequence: g(1)=14−9(1)=14−9=5g(1) = 14 - 9(1) = 14 - 9 = 5. This does not match the first term of the sequence, which should be 1414. Therefore, Aubrey's formula is incorrect.
  7. Correct answer: Since Imran's formula gives the correct terms for the sequence and Aubrey's does not, the correct answer is that only Imran is right.

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