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Find an explicit formula for the geometric sequence 120,60,30,15,dots. Note: the first term should be a(1). a(n)=

Find an explicit formula for the geometric sequence \newline120,60,30,15,…120, 60, 30, 15, \dots. Note: the first term should be \newlinea(1)a(1).\newlinea(n)=a(n)=

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Q. Find an explicit formula for the geometric sequence \newline120,60,30,15,…120, 60, 30, 15, \dots. Note: the first term should be \newlinea(1)a(1).\newlinea(n)=a(n)=
  1. Identify sequence type and first term: Identify the type of sequence and the first term.\newlineThe sequence is 120,60,30,15,…120, 60, 30, 15, \ldots, which is a geometric sequence because each term is obtained by multiplying the previous term by a common ratio. The first term is a(1)=120a(1) = 120.
  2. Find common ratio: Find the common ratio of the sequence.\newlineTo find the common ratio rr, divide the second term by the first term: r=60120=0.5r = \frac{60}{120} = 0.5.
  3. Write explicit formula: Write the explicit formula for the geometric sequence.\newlineThe explicit formula for a geometric sequence is a(n)=a(1)⋅r(n−1)a(n) = a(1) \cdot r^{(n - 1)}. Substitute a(1)=120a(1) = 120 and r=0.5r = 0.5 into the formula to get a(n)=120⋅(0.5)(n−1)a(n) = 120 \cdot (0.5)^{(n - 1)}.

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