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Vera and Fenyang were asked to find an explicit formula for the sequence 26,10,-6,-22,dots, where the first term should be g(1). Vera said the formula is g(n)=26-16(n-1). Fenyang said the formula is g(n)=42-16 n. Which one of them is right? Choose 1 answer: (A) Only Vera (B) Only Fenyang (C) Both Vera and Fenyang (D) Neither Vera nor Fenyang

Vera and Fenyang were asked to find an explicit formula for the sequence 26,10,−6,−22,… 26,10,-6,-22, \ldots , where the first term should be g(1) g(1) .\newlineVera said the formula is g(n)=26−16(n−1) g(n)=26-16(n-1) .\newlineFenyang said the formula is g(n)=42−16n g(n)=42-16 n .\newlineWhich one of them is right?\newlineChoose 11 answer:\newline(A) Only Vera\newline(B) Only Fenyang\newline(C) Both Vera and Fenyang\newline(D) Neither Vera nor Fenyang

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Q. Vera and Fenyang were asked to find an explicit formula for the sequence 26,10,−6,−22,… 26,10,-6,-22, \ldots , where the first term should be g(1) g(1) .\newlineVera said the formula is g(n)=26−16(n−1) g(n)=26-16(n-1) .\newlineFenyang said the formula is g(n)=42−16n g(n)=42-16 n .\newlineWhich one of them is right?\newlineChoose 11 answer:\newline(A) Only Vera\newline(B) Only Fenyang\newline(C) Both Vera and Fenyang\newline(D) Neither Vera nor Fenyang
  1. Identify sequence type and common difference: Identify the type of sequence and the common difference.\newlineThe sequence given is 26,10,−6,−22,…26, 10, -6, -22, \ldots, which appears to be an arithmetic sequence because there is a constant difference between each term. To find the common difference, subtract the second term from the first term: 10−26=−1610 - 26 = -16. The common difference is −16-16.
  2. Test Vera's formula: Test Vera's formula.\newlineVera's formula is g(n)=26−16(n−1)g(n) = 26 - 16(n - 1). To check if Vera's formula is correct, substitute n=1n = 1 to find the first term: g(1)=26−16(1−1)=26−16(0)=26g(1) = 26 - 16(1 - 1) = 26 - 16(0) = 26. This matches the first term of the sequence, so Vera's formula is correct for the first term. Now, check the second term by substituting n=2n = 2: g(2)=26−16(2−1)=26−16=10g(2) = 26 - 16(2 - 1) = 26 - 16 = 10, which also matches the second term of the sequence. Vera's formula seems to be correct so far.
  3. Test Fenyang's formula: Test Fenyang's formula.\newlineFenyang's formula is g(n)=42−16ng(n) = 42 - 16n. To check if Fenyang's formula is correct, substitute n=1n = 1 to find the first term: g(1)=42−16(1)=42−16=26g(1) = 42 - 16(1) = 42 - 16 = 26. This matches the first term of the sequence. Now, check the second term by substituting n=2n = 2: g(2)=42−16(2)=42−32=10g(2) = 42 - 16(2) = 42 - 32 = 10, which also matches the second term of the sequence. Fenyang's formula seems to be correct so far.
  4. Determine correct formula: Determine which formula is correct.\newlineBoth Vera's and Fenyang's formulas have produced the correct first and second terms of the sequence. To determine which formula is correct, we need to check if the formulas will produce the correct terms for all positions nn in the sequence. Since both formulas have given the correct terms for n=1n = 1 and n=2n = 2, and both have the same common difference of −16-16, they will produce the correct terms for all nn. Therefore, both Vera and Fenyang are correct.

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