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Find the 8^th term of the geometric sequence 9,-27,81,dots Answer:

Find the 8th 8^{\text {th }} term of the geometric sequence 9,−27,81,… 9,-27,81, \ldots \newlineAnswer:

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Full solution

Q. Find the 8th 8^{\text {th }} term of the geometric sequence 9,−27,81,… 9,-27,81, \ldots \newlineAnswer:
  1. Identify Sequence Type: Identify the type of sequence and the common ratio.\newlineThe sequence is geometric because 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.\newline−27/9=−3-27 / 9 = -3\newlineCommon Ratio: −3-3
  2. Find Common Ratio: Use the formula for the nth term of a geometric sequence.\newlineThe nth term ana_n of a geometric sequence can be found using the formula an=a1×r(n−1)a_n = a_1 \times r^{(n-1)}, where a1a_1 is the first term, rr is the common ratio, and nn is the term number.\newlineFor the 88th term, a1=9a_1 = 9, r=−3r = -3, and n=8n = 8.
  3. Use nth Term Formula: Calculate the 88th term using the formula.\newlinea8=9×(−3)8−1a_8 = 9 \times (-3)^{8-1}\newlinea8=9×(−3)7a_8 = 9 \times (-3)^7\newlinea8=9×(−2187)a_8 = 9 \times (-2187)\newlinea8=−19683a_8 = -19683

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