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Find an explicit formula for the geometric sequence 3,15,75,375,dots.. Note: the first term should be a(1). a(n)=

Find an explicit formula for the geometric sequence\newline3,15,75,375,…..  3,15,75,375, \ldots \text {.. } \newlineNote: the first term should be a a (11).\newlinea(n)= a(n)=

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Q. Find an explicit formula for the geometric sequence\newline3,15,75,375,…..  3,15,75,375, \ldots \text {.. } \newlineNote: the first term should be a a (11).\newlinea(n)= a(n)=
  1. Identify sequence type: Identify the type of sequence.\newlineThe sequence 3,15,75,375,extellipsis3, 15, 75, 375, extellipsis is a geometric sequence because each term is obtained by multiplying the previous term by a constant ratio rr.
  2. Determine first term: Determine the first term (a1a_1) of the sequence.\newlineThe first term of the sequence is 33.
  3. Calculate common ratio: Calculate the common ratio ( ) of the sequence.\newlineTo find the common ratio, divide the second term by the first term: r=153=5r = \frac{15}{3} = 5.
  4. Write explicit formula: Write the explicit formula for the nth term of the geometric sequence.\newlineThe explicit formula for a geometric sequence is an=a1⋅r(n−1)a_n = a_1 \cdot r^{(n - 1)}. Substitute a1=3a_1 = 3 and r=5r = 5 into the formula to get an=3⋅5(n−1)a_n = 3 \cdot 5^{(n - 1)}.

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