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

Complete the recursive formula of the geometric sequence \newline7,−14,28,−56,…7,-14,28,-56,\dots\newlinea(1)=□a(1)=\square\newlinea(n)=a(n−1)⋅□a(n)=a(n-1) \cdot \square

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Q. Complete the recursive formula of the geometric sequence \newline7,−14,28,−56,…7,-14,28,-56,\dots\newlinea(1)=□a(1)=\square\newlinea(n)=a(n−1)⋅□a(n)=a(n-1) \cdot \square
  1. Find First Term: To find the first term of the geometric sequence, we look at the given sequence. The first term is simply the first number in the sequence. \newlinea(1)=7a(1) = 7
  2. Find Recursive Formula: To find the recursive formula for the geometric sequence, we need to determine the common ratio by dividing any term by the previous term. Let's divide the second term by the first term.\newlineCommon ratio rr = a(2)a(1)\frac{a(2)}{a(1)} = −147\frac{-14}{7} = −2-2
  3. Write Recursive Formula: Now that we have the common ratio, we can write the recursive formula. The recursive formula for a geometric sequence is given by:\newlinea(n)=a(n−1)×ra(n) = a(n-1) \times r\newlineSince we have found that r=−2r = -2, the recursive formula is:\newlinea(n)=a(n−1)×(−2)a(n) = a(n-1) \times (-2)

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