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Find an explicit formula for the geometric sequence 96,24,6,1.5,dots. Note: the first term should be b(1). b(n)=

Find an explicit formula for the geometric sequence\newline96,24,6,1.5,….  96,24,6,1.5, \ldots \text {. } \newlineNote: the first term should be b(1) b(1) .\newlineb(n)= b(n)=

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Q. Find an explicit formula for the geometric sequence\newline96,24,6,1.5,….  96,24,6,1.5, \ldots \text {. } \newlineNote: the first term should be b(1) b(1) .\newlineb(n)= b(n)=
  1. Identify Sequence Type: Identify the type of sequence.\newlineThe sequence 96,24,6,1.5,extellipsis96, 24, 6, 1.5, extellipsis is a geometric sequence because each term is obtained by multiplying the previous term by a constant ratio rr.
  2. Determine First Term and Common Ratio: Determine the first term (b(1)b(1)) and the common ratio (rr).\newlineThe first term is b(1)=96b(1) = 96.\newlineTo find the common ratio, divide the second term by the first term: r=2496=0.25r = \frac{24}{96} = 0.25.
  3. Write Explicit Formula: Write the explicit formula for the geometric sequence.\newlineThe explicit formula for a geometric sequence is b(n)=b(1)⋅r(n−1)b(n) = b(1) \cdot r^{(n - 1)}.\newlineSubstitute b(1)=96b(1) = 96 and r=0.25r = 0.25 into the formula.\newlineb(n)=96⋅(0.25)(n−1)b(n) = 96 \cdot (0.25)^{(n - 1)}.

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