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Find an explicit formula for the geometric sequence -9,-18,-36,-72,dots Note: the first term should be c(1). c(n)=

Find an explicit formula for the geometric sequence −9,−18,−36,−72,…-9,-18,-36,-72,\dots Note: the first term should be c(1)c(1).\newlinec(n)=c(n)=

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Q. Find an explicit formula for the geometric sequence −9,−18,−36,−72,…-9,-18,-36,-72,\dots Note: the first term should be c(1)c(1).\newlinec(n)=c(n)=
  1. Identify sequence type and first term: Identify the type of sequence and the first term.\newlineThe sequence is −9,−18,−36,−72,…-9, -18, -36, -72, \ldots, which is a geometric sequence because each term is obtained by multiplying the previous term by a common ratio. The first term is c(1)=−9c(1) = -9.
  2. Determine common ratio: Determine the common ratio rr of the sequence.\newlineTo find the common ratio, divide the second term by the first term: r=−18−9=2r = \frac{-18}{-9} = 2.
  3. Write explicit formula: Write the explicit formula for the geometric sequence.\newlineThe explicit formula for a geometric sequence is c(n)=c(1)⋅r(n−1)c(n) = c(1) \cdot r^{(n - 1)}. Substitute c(1)=−9c(1) = -9 and r=2r = 2 into the formula.\newlinec(n)=−9⋅2(n−1)c(n) = -9 \cdot 2^{(n - 1)}.

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