Priyanka and Ethan were asked to find an explicit formula for the sequence -3,-14,-25,-36,dots, where the first term should be g(1). Priyanka said the formula is g(n)=-3-11 n. Ethan said the formula is g(n)=-3+11 n. Which one of them is right? Choose 1 answer: (A) Only Priyanka (B) Only Ethan (C) Both Priyanka and Ethan (D) Neither Priyanka nor Ethan

Question

Priyanka and Ethan were asked to find an explicit formula for the sequence  -3,-14,-25,-36,dots, where the first term should be  g(1). Priyanka said the formula is  g(n)=-3-11 n. Ethan said the formula is  g(n)=-3+11 n. Which one of them is right? Choose 1 answer: (A) Only Priyanka (B) Only Ethan (C) Both Priyanka and Ethan (D) Neither Priyanka nor Ethan

Bytelearn · Accepted Answer

Analyze Sequence Pattern: To determine the correct formula, we need to analyze the pattern of the sequence. We will look at the difference between consecutive terms to find the common difference.Calculate Common Difference: The difference between the first and second term is -14 - (-3) = -11. The difference between the second and third term is -25 - (-14) = -11. The difference between the third and fourth term is -36 - (-25) = -11. This shows that the sequence is arithmetic with a common difference of -11.Write Explicit Formula: Now we will use the common difference to write the explicit formula. The nth term of an arithmetic sequence can be found using the formula g(n) = a + (n - 1)d, where a is the first term and d is the common difference.Substitute Values: Substituting the values we have, a = -3 (the first term) and d = -11 (the common difference), into the formula, we get g(n) = -3 + (n - 1)(-11).Simplify Formula: Simplifying the formula, we get g(n) = -3 - 11(n - 1). Expanding the formula, we get g(n) = -3 - 11n + 11.Combine Like Terms: Further simplifying, we combine like terms to get g(n) = -3 - 11n + 11 = -11n + 8.

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