Khaled and Wilma were asked to find an explicit formula for the sequence 1,3,9,27,dots, where the first term should be f(1). Khaled said the formula is f(n)=1*3^(n-1), and Wilma said the formula is f(n)=1*3^(n). Which one of them is right? Choose 1 answer: (A) Only Khaled (B) Only Wilma (c) Both Khaled and Wilma (D) Neither Khaled nor Wilma

Question

Khaled and Wilma were asked to find an explicit formula for the sequence  1,3,9,27,dots, where the first term should be  f(1). Khaled said the formula is  f(n)=1*3^(n-1), and Wilma said the formula is  f(n)=1*3^(n). Which one of them is right? Choose 1 answer: (A) Only Khaled (B) Only Wilma (c) Both Khaled and Wilma (D) Neither Khaled nor Wilma

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Determine Khaled's formula: We need to determine which formula correctly represents the given geometric sequence. The sequence is 1, 3, 9, 27, ..., which means each term is multiplied by a common ratio to get the next term. Let's check Khaled's formula first.Test Khaled's formula with first term: Khaled's formula is f(n) = 1 * 3^(n-1). Let's test this formula with the first term where n = 1. If Khaled is correct, f(1) should equal 1. Calculation: f(1) = 1 * 3^(1-1) = 1 * 3^0 = 1 * 1 = 1. Since the first term of the sequence is indeed 1, Khaled's formula correctly calculates the first term.Test Khaled's formula with second term: Now let's test Khaled's formula with the second term where n = 2. If Khaled is correct, f(2) should equal 3. Calculation: f(2) = 1 * 3^(2-1) = 1 * 3^1 = 1 * 3 = 3. Since the second term of the sequence is indeed 3, Khaled's formula correctly calculates the second term.Test Khaled's formula with third term: Let's test Khaled's formula with the third term where n = 3. If Khaled is correct, f(3) should equal 9. Calculation: f(3) = 1 * 3^(3-1) = 1 * 3^2 = 1 * 9 = 9. Since the third term of the sequence is indeed 9, Khaled's formula correctly calculates the third term.Check Wilma's formula: Now let's check Wilma's formula, which is f(n) = 1 * 3^n. We'll test this formula with the first term where n = 1. If Wilma is correct, f(1) should equal 1. Calculation: f(1) = 1 * 3^1 = 1 * 3 = 3. Since the first term of the sequence is 1, not 3, Wilma's formula does not correctly calculate the first term.Conclusion: Only Khaled's formula is correct: Since Wilma's formula did not correctly calculate the first term, we do not need to test it further. We can conclude that only Khaled's formula is correct.

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