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Complete the recursive formula of the geometric sequence 27,-9,3,-1,dots".. " b(1)= b(n)=b(n-1)". "

Complete the recursive formula of the geometric sequence\newline27,−9,3,−1,….  27,-9,3,-1, \ldots \text {. } \newlineb(1)=□ b(1)=\square \newlineb(n)=b(n−1)⋅□ b(n)=b(n-1) \cdot \square

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Q. Complete the recursive formula of the geometric sequence\newline27,−9,3,−1,….  27,-9,3,-1, \ldots \text {. } \newlineb(1)=□ b(1)=\square \newlineb(n)=b(n−1)⋅□ b(n)=b(n-1) \cdot \square
  1. Identify Pattern: We have the sequence: 27,−9,3,−1,…27, -9, 3, -1, \ldots\newlineTo find the recursive formula, we need to determine the pattern between consecutive terms.
  2. First Term Given: The first term is given as b(1)=27b(1) = 27.
  3. Calculate Common Ratio: To find the common ratio rr, we divide the second term by the first term: r=(−9)/27=−1/3r = (-9) / 27 = -1/3.
  4. Write Recursive Formula: Now that we have the common ratio, we can write the recursive formula. The recursive formula for a geometric sequence is b(n)=b(n−1)×rb(n) = b(n-1) \times r.
  5. Substitute Common Ratio: Substitute the common ratio (−13)(-\frac{1}{3}) into the recursive formula: b(n)=b(n−1)×(−13)b(n) = b(n-1) \times (-\frac{1}{3}).

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