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Complete the recursive formula of the geometric sequence -0.6,3,-15,75,dots. c(1)= c(n)=c(n-1).

Complete the recursive formula of the geometric sequence \newline−0.6,3,−15,75,…-0.6, 3, -15, 75, \dots.\newlinec(1)=c(1)= \newlinec(n)=c(n−1)⋅c(n)=c(n-1)\cdot

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Q. Complete the recursive formula of the geometric sequence \newline−0.6,3,−15,75,…-0.6, 3, -15, 75, \dots.\newlinec(1)=c(1)= \newlinec(n)=c(n−1)⋅c(n)=c(n-1)\cdot
  1. Identify first term and common ratio: We need to identify the first term and the common ratio of the sequence. The first term is given directly as −0.6-0.6.
  2. Calculate common ratio: To find the common ratio rr, we divide the second term by the first term: r=3(−0.6)=−5r = \frac{3}{(-0.6)} = -5.
  3. Write recursive formula: Now that we have the first term and the common ratio, we can write the recursive formula. The recursive formula for a geometric sequence is given by c(n)=c(n−1)×rc(n) = c(n-1) \times r, where c(1)c(1) is the first term and rr is the common ratio.
  4. Substitute values into formula: Substitute the known values into the recursive formula. The first term c(1)=−0.6c(1) = -0.6, and the common ratio r=−5r = -5. Therefore, the recursive formula is:\newlinec(1)=−0.6c(1) = -0.6\newlinec(n)=c(n−1)×(−5)c(n) = c(n-1) \times (-5) for n > 1

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