Q. Complete the recursive formula of the geometric sequence−125,−25,−5,−1,….b(1)=□b(n)=b(n−1)⋅□
Identify First Term: Identify the first term of the sequence.The first term of the sequence is given as b(1)=−125.
Determine Common Ratio: Determine the common ratio by dividing the second term by the first term.The common ratio r can be found by dividing the second term −25 by the first term −125.r=−125−25=51
Write Recursive Formula: Write the recursive formula using the first term and the common ratio.The recursive formula for a geometric sequence is b(n)=b(n−1)×r, where r is the common ratio.Since we have b(1)=−125 and r=51, the recursive formula is:b(n)=b(n−1)×(51)
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