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Wang Lei and Amira were asked to find an explicit formula for the sequence 30,150,750,3750,dots, where the first term should be g(1). Wang Lei said the formula is g(n)=30*5^(n-1), and Amira said the formula is g(n)=6*5^(n). Which one of them is right? Choose 1 answer: (A) Only Wang Lei (B) Only Amira (c) Both Wang Lei and Amira (D) Neither Wang Lei nor Amira

Wang Lei and Amira were asked to find an explicit formula for the sequence \newline30,150,750,3750,…30, 150, 750, 3750, \dots, where the first term should be \newlineg(1)g(1).\newlineWang Lei said the formula is \newlineg(n)=30⋅5(n−1)g(n) = 30 \cdot 5^{(n-1)}, and\newlineAmira said the formula is \newlineg(n)=6⋅5ng(n) = 6 \cdot 5^n.\newlineWhich one of them is right?\newlineChoose 11 answer:\newline(A) Only Wang Lei\newline(B) Only Amira\newline(C) Both Wang Lei and Amira\newline(D) Neither Wang Lei nor Amira

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Q. Wang Lei and Amira were asked to find an explicit formula for the sequence \newline30,150,750,3750,…30, 150, 750, 3750, \dots, where the first term should be \newlineg(1)g(1).\newlineWang Lei said the formula is \newlineg(n)=30⋅5(n−1)g(n) = 30 \cdot 5^{(n-1)}, and\newlineAmira said the formula is \newlineg(n)=6⋅5ng(n) = 6 \cdot 5^n.\newlineWhich one of them is right?\newlineChoose 11 answer:\newline(A) Only Wang Lei\newline(B) Only Amira\newline(C) Both Wang Lei and Amira\newline(D) Neither Wang Lei nor Amira
  1. Analyze sequence type: Analyze the sequence to determine if it is arithmetic or geometric.\newlineThe sequence is 30,150,750,3750,…30, 150, 750, 3750, \ldots\newlineTo determine if the sequence is arithmetic or geometric, we look at the ratio of consecutive terms.\newline15030=5\frac{150}{30} = 5\newline750150=5\frac{750}{150} = 5\newline3750750=5\frac{3750}{750} = 5\newlineSince each term is multiplied by 55 to get the next term, the sequence is geometric.
  2. Determine first term and common ratio: Determine the first term and the common ratio of the sequence.\newlineThe first term g(1)g(1) is 3030.\newlineThe common ratio rr is the factor we multiply by to get from one term to the next, which we have determined to be 55.
  3. Evaluate Wang Lei's formula: Evaluate Wang Lei's formula.\newlineWang Lei's formula is g(n)=30⋅5(n−1)g(n) = 30 \cdot 5^{(n-1)}.\newlineLet's check if this formula works for the first few terms:\newlineFor n=1n = 1: g(1)=30⋅5(1−1)=30⋅50=30⋅1=30g(1) = 30 \cdot 5^{(1-1)} = 30 \cdot 5^0 = 30 \cdot 1 = 30\newlineFor n=2n = 2: g(2)=30⋅5(2−1)=30⋅51=30⋅5=150g(2) = 30 \cdot 5^{(2-1)} = 30 \cdot 5^1 = 30 \cdot 5 = 150\newlineFor n=3n = 3: g(3)=30⋅5(3−1)=30⋅52=30⋅25=750g(3) = 30 \cdot 5^{(3-1)} = 30 \cdot 5^2 = 30 \cdot 25 = 750\newlineWang Lei's formula correctly generates the sequence.
  4. Evaluate Amira's formula: Evaluate Amira's formula.\newlineAmira's formula is g(n)=6⋅5ng(n) = 6 \cdot 5^n.\newlineLet's check if this formula works for the first few terms:\newlineFor n=1n = 1: g(1)=6⋅51=6⋅5=30g(1) = 6 \cdot 5^1 = 6 \cdot 5 = 30\newlineFor n=2n = 2: g(2)=6⋅52=6⋅25=150g(2) = 6 \cdot 5^2 = 6 \cdot 25 = 150\newlineFor n=3n = 3: g(3)=6⋅53=6⋅125=750g(3) = 6 \cdot 5^3 = 6 \cdot 125 = 750\newlineAmira's formula also correctly generates the sequence.

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