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Write an explicit formula for a_(n), the n^("th ") term of the sequence 2,6,18,dots Answer: a_(n)=

Write an explicit formula for an a_{n} , the nth  n^{\text {th }} term of the sequence 2,6,18,… 2,6,18, \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 2,6,18,… 2,6,18, \ldots \newlineAnswer: an= a_{n}=
  1. Identify Geometric Sequence: The given sequence is 2,6,18,…2, 6, 18, \ldots which appears to be a geometric sequence where each term is multiplied by a common ratio to get the next term. To find the common ratio, divide the second term by the first term.\newlineCommon ratio (r)=62=3(r) = \frac{6}{2} = 3
  2. Calculate Common Ratio: The first term of the sequence a1a_1 is 22. The nnth term of a geometric sequence is given by the formula an=a1⋅r(n−1)a_n = a_1 \cdot r^{(n-1)}, where rr is the common ratio and nn is the term number.
  3. Find nth Term Formula: Substitute the known values into the formula to get the nth term. an=2×3(n−1)a_n = 2 \times 3^{(n-1)}

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