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Write an explicit formula for a_(n), the n^("th ") term of the sequence 5,-10,20,dots Answer: a_(n)=

Write an explicit formula for an a_{n} , the nth  n^{\text {th }} term of the sequence 5,−10,20,… 5,-10,20, \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 5,−10,20,… 5,-10,20, \ldots \newlineAnswer: an= a_{n}=
  1. Identify Sequence Type: Identify whether the given sequence is geometric or arithmetic. The sequence 5,−10,20,…5, -10, 20, \ldots has a common ratio between consecutive terms, as each term is multiplied by −2-2 to get the next term. Therefore, 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 \cdot r^{(n-1)}, where a1a_1 is the first term and rr is the common ratio. For the sequence 5,−10,20,…5, -10, 20, \ldots, the first term, a1a_1, is 55 and the common ratio, rr, is −2-2.
  3. Substitute Values: Substitute the values of a1a_1 and rr into the formula to write an expression to describe the sequence. The expression for the sequence 5,−10,20,…5, -10, 20, \ldots is an=5×(−2)(n−1)a_n = 5 \times (-2)^{(n-1)}.

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