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Complete the recursive formula of the geometric sequence 56,-28,14,-7,dots.. d(1)= d(n)=d(n-1)". "

Complete the recursive formula of the geometric sequence \newline56,−28,14,−7,…56,-28,14,-7,\dots.\newlined(1)=d(1)=\newlined(n)=d(n−1)⋅d(n)=d(n-1)\cdot

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Full solution

Q. Complete the recursive formula of the geometric sequence \newline56,−28,14,−7,…56,-28,14,-7,\dots.\newlined(1)=d(1)=\newlined(n)=d(n−1)⋅d(n)=d(n-1)\cdot
  1. Identify Common Ratio: To find the recursive formula for the geometric sequence, we first need to identify the common ratio by dividing any term by the term before it.\newlineLet's divide the second term by the first term: −28÷56=−0.5-28 \div 56 = -0.5
  2. Write Recursive Formula: Now that we have the common ratio, we can write the recursive formula. The first term d(1)d(1) is given as 5656. So, d(1)=56d(1) = 56
  3. Calculate Recursive Part: For the recursive part, we know that each term is −0.5-0.5 times the previous term. Therefore, the recursive formula will be:\newlined(n)=d(n−1)×−0.5d(n) = d(n-1) \times -0.5 for n>1n > 1

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