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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)=2.7,g(n)=g(n−1)×6.1\begin{cases} g(1)=2.7, g(n)=g(n-1)\times 6.1 \end{cases} Find an explicit formula for g(n)g(n).g(n)=g(n)=

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Q. {g(1)=2.7,g(n)=g(n−1)×6.1\begin{cases} g(1)=2.7, g(n)=g(n-1)\times 6.1 \end{cases} Find an explicit formula for g(n)g(n).g(n)=g(n)=
  1. Given Information: We are given the initial value of the function g(1)=2.7g(1) = 2.7 and the recursive formula g(n)=g(n−1)×6.1g(n) = g(n-1) \times 6.1. This indicates that the sequence is geometric, where each term is obtained by multiplying the previous term by the common ratio 6.16.1.
  2. Identifying First Term and Common Ratio: To find an explicit formula for g(n), we need to identify the first term (a1a_1) and the common ratio (rr) of the geometric sequence. From the given information, we have:\newlinea1=g(1)=2.7a_1 = g(1) = 2.7\newliner=6.1r = 6.1
  3. Explicit Formula for Geometric Sequence: The explicit formula for a geometric sequence is given by:\newlineg(n) = a11 ×r(n−1) \times r^{(n - 1)} \newlineSubstituting the values of a11 and r, we get:\newlineg(n) = 2.7×6.1(n−1)2.7 \times 6.1^{(n - 1)}

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