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Write an explicit formula for a_(n), the n^("th ") term of the sequence 144,24,4,dots Answer: a_(n)=

Write an explicit formula for an a_{n} , the nth  n^{\text {th }} term of the sequence 144,24,4,… 144,24,4, \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 144,24,4,… 144,24,4, \ldots \newlineAnswer: an= a_{n}=
  1. Identify Sequence Type: Identify whether the given sequence is geometric or arithmetic. The sequence 144144, 2424, 44, ... has a common ratio between consecutive terms, so it is a geometric sequence.
  2. Use Explicit Formula: Use the explicit formula for a geometric sequence, an=a1×r(n−1)a_n = a_1 \times r^{(n-1)}, where a1a_1 is the first term and rr is the common ratio. For the sequence 144,24,4,…144, 24, 4, \ldots, the first term, a1a_1, is 144144 and the common ratio, rr, can be found by dividing the second term by the first term: r=24144=16r = \frac{24}{144} = \frac{1}{6}.
  3. Substitute Values: Substitute the values of a1a_{1} and rr into the formula to write an explicit formula for the nnth term of the sequence. The expression for the sequence 144,24,4,…144, 24, 4, \ldots is an=144×(1/6)n−1a_{n} = 144 \times (1/6)^{n-1}.

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