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{[g(1)=2.7],[g(n)=g(n-1)*6.1]:} Find an explicit formula for g(n). g(n)= ◻

{g(1)=2.7g(n)=g(n−1)⋅6.1 \left\{\begin{array}{l} g(1)=2.7 \\ g(n)=g(n-1) \cdot 6.1 \end{array}\right. \newlineFind an explicit formula for g(n) g(n) .\newlineg(n)= g(n)= \newline□ \square

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Q. {g(1)=2.7g(n)=g(n−1)⋅6.1 \left\{\begin{array}{l} g(1)=2.7 \\ g(n)=g(n-1) \cdot 6.1 \end{array}\right. \newlineFind an explicit formula for g(n) g(n) .\newlineg(n)= g(n)= \newline□ \square
  1. Base Case Given: We know g(1)=2.7g(1) = 2.7, this is our base case.
  2. Recursive Formula: The recursive formula is g(n)=g(n−1)×6.1g(n) = g(n-1) \times 6.1, which means each term is 6.16.1 times the previous term.
  3. Finding Explicit Formula: To find an explicit formula, we need to express g(n)g(n) in terms of nn and the base case g(1)g(1).
  4. Calculating g(2)g(2): Since g(n)=g(n−1)×6.1g(n) = g(n-1) \times 6.1, we can write g(2)=g(1)×6.1g(2) = g(1) \times 6.1.
  5. Multiplication Pattern: So, g(2)=2.7×6.1g(2) = 2.7 \times 6.1.
  6. Final Explicit Formula: Calculating g(2)g(2) gives us g(2)=16.47g(2) = 16.47, but we don't need this value for the explicit formula.
  7. Final Explicit Formula: Calculating g(2)g(2) gives us g(2)=16.47g(2) = 16.47, but we don't need this value for the explicit formula.We see that each step multiplies by 6.16.1, so g(n)=g(1)×6.1(n−1)g(n) = g(1) \times 6.1^{(n-1)}.
  8. Final Explicit Formula: Calculating g(2)g(2) gives us g(2)=16.47g(2) = 16.47, but we don't need this value for the explicit formula.We see that each step multiplies by 6.16.1, so g(n)=g(1)×6.1(n−1)g(n) = g(1) \times 6.1^{(n-1)}.Substitute g(1)=2.7g(1) = 2.7 into the formula to get g(n)=2.7×6.1(n−1)g(n) = 2.7 \times 6.1^{(n-1)}.

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