Felipe and Ling were asked to find an explicit formula for the sequence 24,16,8,0,dots, where the first term should be f(1). Felipe said the formula is f(n)=32-8n. Ling said the formula is f(n)=24-8n. Which one of them is right? Choose 1 answer: (A) Only Felipe (B) Only Ling (C) Both Felipe and Ling (D) Neither Felipe nor Ling

Question

Felipe and Ling were asked to find an explicit formula for the sequence  24,16,8,0,dots, where the first term should be  f(1). Felipe said the formula is  f(n)=32-8n. Ling said the formula is  f(n)=24-8n. Which one of them is right? Choose 1 answer: (A) Only Felipe (B) Only Ling (C) Both Felipe and Ling (D) Neither Felipe nor Ling

Bytelearn · Accepted Answer

Identify pattern: Identify the pattern in the sequence to determine if it is arithmetic or geometric. The sequence 24, 16, 8, 0, ... decreases by 8 each time, which indicates it is an arithmetic sequence with a common difference of -8.Use explicit formula: Use the explicit formula for an arithmetic sequence, which is f(n) = f(1) + (n-1)d, where f(1) is the first term and d is the common difference. For this sequence, f(1) is 24 and the common difference d is -8.Substitute values: Substitute the values of f(1) and d into the formula to find the explicit formula for the sequence. The formula becomes f(n) = 24 + (n-1)(-8).Simplify formula: Simplify the formula by distributing the -8 inside the parentheses. This gives us f(n) = 24 - 8n + 8.Combine like terms: Combine like terms in the formula to get the final explicit formula. This results in f(n) = 32 - 8n.Compare with Felipe and Ling: Compare the derived formula with the formulas provided by Felipe and Ling. Felipe's formula is f(n) = 32 - 8n, which matches our derived formula. Ling's formula is f(n) = 24 - 8n, which does not match our derived formula.

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