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Complete the recursive formula of the geometric sequence {:[-0.56","-5.6","-56","-560","dots.],[c(1)=],[c(n)=c(n-1).]:}

Complete the recursive formula of the geometric sequence\newline−0.56,−5.6,−56,−560,….c(1)=□c(n)=c(n−1)⋅□ \begin{array}{l} -0.56,-5.6,-56,-560, \ldots . \\ c(1)=\square \\ c(n)=c(n-1) \cdot \square \end{array}

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Q. Complete the recursive formula of the geometric sequence\newline−0.56,−5.6,−56,−560,….c(1)=□c(n)=c(n−1)⋅□ \begin{array}{l} -0.56,-5.6,-56,-560, \ldots . \\ c(1)=\square \\ c(n)=c(n-1) \cdot \square \end{array}
  1. Calculate Common Ratio: We are given the sequence: −0.56,−5.6,−56,−560,…-0.56, -5.6, -56, -560, \ldots\newlineTo find the recursive formula, we need to determine the common ratio (r)(r) by dividing any term by the previous term.\newlineLet's divide the second term by the first term to find the common ratio.\newliner=−5.6−0.56r = \frac{-5.6}{-0.56}
  2. Find Value of r: Now, let's perform the calculation to find the value of r.\newliner=(−5.6)/(−0.56)=10r = (-5.6) / (-0.56) = 10
  3. Determine Recursive Formula: The recursive formula for a geometric sequence is given by:\newlinec(n)=c(n−1)×rc(n) = c(n-1) \times r\newlineWe have found that r=10r = 10. Now we need to provide the first term of the sequence to complete the recursive formula.\newlineThe first term is given as c(1)=−0.56c(1) = -0.56.
  4. Provide First Term: The recursive formula for the given sequence is:\newlinec(1)=−0.56c(1) = -0.56\newlinec(n)=c(n−1)×10c(n) = c(n-1) \times 10 for n>1n > 1

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