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Ivy and Andrey were asked to find an explicit formula for the sequence -100,-50,0,50,dots, where the first term should be f(1). Ivy said the formula is f(n)=-100+50(n-1). Andrey said the formula is f(n)=-150+50 n. Which one of them is right? Choose 1 answer: (A) Only Ivy (B) Only Andrey (C) Both Ivy and Andrey (D) Neither Ivy nor Andrey

Ivy and Andrey were asked to find an explicit formula for the sequence −100,−50,0,50,… -100,-50,0,50, \ldots , where the first term should be f(1) f(1) .\newlineIvy said the formula is f(n)=−100+50(n−1) f(n)=-100+50(n-1) .\newlineAndrey said the formula is f(n)=−150+50n f(n)=-150+50 n .\newlineWhich one of them is right?\newlineChoose 11 answer:\newline(A) Only Ivy\newline(B) Only Andrey\newline(C) Both Ivy and Andrey\newline(D) Neither Ivy nor Andrey

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Q. Ivy and Andrey were asked to find an explicit formula for the sequence −100,−50,0,50,… -100,-50,0,50, \ldots , where the first term should be f(1) f(1) .\newlineIvy said the formula is f(n)=−100+50(n−1) f(n)=-100+50(n-1) .\newlineAndrey said the formula is f(n)=−150+50n f(n)=-150+50 n .\newlineWhich one of them is right?\newlineChoose 11 answer:\newline(A) Only Ivy\newline(B) Only Andrey\newline(C) Both Ivy and Andrey\newline(D) Neither Ivy nor Andrey
  1. Identify sequence type: Identify the type of sequence. The sequence −100,−50,0,50,…-100, -50, 0, 50, \ldots has a common difference between consecutive terms, which means it is an arithmetic sequence.
  2. Determine first term and common difference: Determine the first term (f(1)f(1)) and the common difference (dd) of the sequence. The first term is −100-100 and the common difference is the difference between any two consecutive terms, which is 5050.
  3. Use explicit formula: Use the explicit formula for an arithmetic sequence, f(n)=f(1)+(n−1)df(n) = f(1) + (n-1)d, where f(1)f(1) is the first term and dd is the common difference. Substitute the values of f(1)f(1) and dd into the formula. The formula becomes f(n)=−100+(n−1)×50f(n) = -100 + (n-1)\times50.
  4. Simplify formula: Simplify the formula from Step 33. The formula simplifies to f(n)=−100+50n−50f(n) = -100 + 50n - 50, which further simplifies to f(n)=50n−150f(n) = 50n - 150.
  5. Compare with Ivy and Andrey: Compare the simplified formula from Step 44 with the formulas provided by Ivy and Andrey. Ivy's formula is f(n)=−100+50(n−1)f(n) = -100 + 50(n-1), which simplifies to f(n)=50n−150f(n) = 50n - 150. Andrey's formula is f(n)=−150+50nf(n) = -150 + 50n, which is already simplified and is the same as Ivy's simplified formula.
  6. Determine correct formula: Determine which of them is right based on the comparison in Step 55. Since both Ivy's and Andrey's formulas simplify to the same correct formula for the sequence, both of them are right.

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