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Find an explicit formula for the geometric sequence -25,-50,-100,-200,dots.. Note: the first term should be d(1). d(n)=

Find an explicit formula for the geometric sequence −25,−50,−100,−200,…-25,-50,-100,-200,\dots. Note: the first term should be d(1)d(1).\newlined(n)=d(n)=

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Q. Find an explicit formula for the geometric sequence −25,−50,−100,−200,…-25,-50,-100,-200,\dots. Note: the first term should be d(1)d(1).\newlined(n)=d(n)=
  1. Identify sequence type: Identify the type of sequence.\newlineThe sequence is −25-25, −50-50, −100-100, −200-200, extellipsis \newlineEach term is obtained by multiplying the previous term by a common ratio.\newlineThis is a geometric sequence.
  2. Determine first term and common ratio: Determine the first term d(1)d(1) and the common ratio rr.\newlineThe first term d(1)d(1) is −25-25.\newlineTo find the common ratio, divide the second term by the first term: r=−50−25=2r = \frac{-50}{-25} = 2.
  3. Write explicit formula for geometric sequence: Write the explicit formula for the geometric sequence using d(1)d(1) and rr. The explicit formula for a geometric sequence is d(n)=d(1)⋅r(n−1)d(n) = d(1) \cdot r^{(n - 1)}. Substitute d(1)=−25d(1) = -25 and r=2r = 2 into the formula. d(n)=−25⋅2(n−1)d(n) = -25 \cdot 2^{(n - 1)}.

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