Gustavo and Yuki were asked to find an explicit formula for the sequence 19,0,-19,-38,dots, where the first term should be h(1). Gustavo said the formula is h(n)=19-19 n. Yuki said the formula is h(n)=-19+19 n. Which one of them is right? Choose 1 answer: (A) Only Gustavo (B) Only Yuki (c) Both Gustavo and Yuki (D) Neither Gustavo nor Yuki

Question

Gustavo and Yuki were asked to find an explicit formula for the sequence  19,0,-19,-38,dots, where the first term should be  h(1). Gustavo said the formula is  h(n)=19-19 n. Yuki said the formula is  h(n)=-19+19 n. Which one of them is right? Choose 1 answer: (A) Only Gustavo (B) Only Yuki (c) Both Gustavo and Yuki (D) Neither Gustavo nor Yuki

Bytelearn · Accepted Answer

Identify the pattern: Identify the pattern in the sequence. The sequence 19, 0, -19, -38, ... decreases by 19 each time. This indicates that it is an arithmetic sequence with a common difference of -19.Use explicit formula: Use the explicit formula for an arithmetic sequence, h(n) = h(1) + (n-1)d, where h(1) is the first term and d is the common difference. For the sequence 19, 0, -19, -38, ..., the first term, h(1), is 19 and the common difference, d, is -19.Write expression for sequence: Substitute the values of h(1) and d into the formula to write an expression to describe the sequence. The expression for the sequence is h(n) = 19 + (n-1)(-19), which simplifies to h(n) = 19 - 19n + 19, and then further simplifies to h(n) = 19 - 19n + 19.

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