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Write an explicit formula for a_(n), the n^("th ") term of the sequence 3,6,12,dots Answer: a_(n)=

Write an explicit formula for an a_{n} , the nth  n^{\text {th }} term of the sequence 3,6,12,… 3,6,12, \ldots \newlineAnswer: an= a_{n}=

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Q. Write an explicit formula for an a_{n} , the nth  n^{\text {th }} term of the sequence 3,6,12,… 3,6,12, \ldots \newlineAnswer: an= a_{n}=
  1. Identify Geometric Sequence: The given sequence is 3,6,12,…3, 6, 12, \ldots which is a geometric sequence where each term is twice the previous term. This means the common ratio (r)(r) is 22.
  2. Find First Term: The first term of the sequence a1a_1 is 33. Since this is a geometric sequence, the nth term is given by the formula an=a1⋅r(n−1)a_n = a_1 \cdot r^{(n-1)}.
  3. Apply Formula: Substitute the known values into the formula to get an=3×2(n−1)a_n = 3 \times 2^{(n-1)}.
  4. Simplify Formula: Simplify the formula to get the explicit formula for the nthn^{th} term of the sequence: an=3×2(n−1)a_n = 3 \times 2^{(n-1)}.

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