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Complete the recursive formula of the geometric sequence {:[0.2","-1","5","-25","dots.],[a(1)=],[a(n)=a(n-1).]:}

Complete the recursive formula of the geometric sequence 0.2,−1,5,−25,… 0.2,-1,5,-25, \ldots .\newlinea(1)=□ a(1)= \square \newlinea(n)=a(n−1)⋅□ a(n)=a(n-1) \cdot \square

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Q. Complete the recursive formula of the geometric sequence 0.2,−1,5,−25,… 0.2,-1,5,-25, \ldots .\newlinea(1)=□ a(1)= \square \newlinea(n)=a(n−1)⋅□ a(n)=a(n-1) \cdot \square
  1. Calculate Common Ratio: We are given the sequence 0.2,−1,5,−25,…0.2, -1, 5, -25, \ldots and the first term a(1)=0.2a(1) = 0.2. To find the recursive formula, we need to determine the common ratio by dividing the second term by the first term.\newlineCalculation: r=a(2)a(1)=−10.2=−5r = \frac{a(2)}{a(1)} = \frac{-1}{0.2} = -5
  2. Write Recursive Formula: Now that we have the common ratio r=−5r = -5, we can write the recursive formula. The recursive formula for a geometric sequence is given by a(n)=a(n−1)×ra(n) = a(n-1) \times r, where rr is the common ratio.\newlineCalculation: a(n)=a(n−1)×(−5)a(n) = a(n-1) \times (-5)

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