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Find an explicit formula for the geometric sequence −1,−7,−49,−343-1, -7, -49, -343 the first term should be b(1)b(1)

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Q. Find an explicit formula for the geometric sequence −1,−7,−49,−343-1, -7, -49, -343 the first term should be b(1)b(1)
  1. Identify Sequence Type: Identify the type of sequence.\newlineThe sequence −1-1, −7-7, −49-49, −343-343, ... appears to be geometric because each term is obtained by multiplying the previous term by a common ratio.
  2. Find First Term and Ratio: Determine the first term b(1)b(1) and the common ratio rr of the sequence.\newlineFirst term: b(1)=−1b(1) = -1\newlineTo find the common ratio, divide the second term by the first term: r=−7−1=7r = \frac{-7}{-1} = 7
  3. Formulate Explicit Formula: Formulate the explicit formula for the geometric sequence using b(1)b(1) and rr. The general formula for the nnth term of a geometric sequence is b(n)=b(1)⋅r(n−1)b(n) = b(1) \cdot r^{(n - 1)}. Substitute −1-1 for b(1)b(1) and 77 for rr to get the explicit formula. b(n)=−1⋅7(n−1)b(n) = -1 \cdot 7^{(n - 1)}

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