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Complete the recursive formula of the geometric sequence {:[-0.3","0.9","-2.7","8.1","dots],[b(1)=],[b(n)=b(n-1)]:}

Complete the recursive formula of the geometric sequence\newline−0.3,0.9,−2.7,8.1,….b(1)=□b(n)=b(n−1)⋅□ \begin{array}{l} -0.3,0.9,-2.7,8.1, \ldots . \\ b(1)=\square \\ b(n)=b(n-1) \cdot \square \end{array}

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Q. Complete the recursive formula of the geometric sequence\newline−0.3,0.9,−2.7,8.1,….b(1)=□b(n)=b(n−1)⋅□ \begin{array}{l} -0.3,0.9,-2.7,8.1, \ldots . \\ b(1)=\square \\ b(n)=b(n-1) \cdot \square \end{array}
  1. Given Sequence: We are given the first few terms of a geometric sequence: −0.3-0.3, 0.90.9, −2.7-2.7, 8.18.1, ...\newlineTo find the recursive formula, we need to determine the common ratio (rr) by dividing any term by the previous term.\newlineLet's divide the second term by the first term to find rr.\newliner=0.9−0.3=−3r = \frac{0.9}{-0.3} = -3
  2. Find Common Ratio: Now that we have the common ratio, we can write the recursive formula.\newlineWe are given the first term b(1)=−0.3b(1) = -0.3.\newlineThe recursive formula is b(n)=b(n−1)×rb(n) = b(n-1) \times r, where rr is the common ratio.\newlineSubstitute r=−3r = -3 into the formula.\newlineb(n)=b(n−1)×(−3)b(n) = b(n-1) \times (-3)

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