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Find the 10^th term of the geometric sequence 5,-25,125,dots Answer:

Find the 10th 10^{\text {th }} term of the geometric sequence 5,−25,125,… 5,-25,125, \ldots \newlineAnswer:

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Full solution

Q. Find the 10th 10^{\text {th }} term of the geometric sequence 5,−25,125,… 5,-25,125, \ldots \newlineAnswer:
  1. Identify type and ratio: Identify the type of sequence and the common ratio.\newlineThe given sequence is geometric because each term is multiplied by a common ratio to get the next term.\newlineTo find the common ratio, divide the second term by the first term.\newlineCommon Ratio rr = −25/5=−5-25 / 5 = -5
  2. Use nth term formula: 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 \cdot r^{(n-1)}, where a1a_1 is the first term and rr is the common ratio.\newlineWe want to find the 1010th term a10a_{10}, so n=10n = 10.
  3. Substitute values: Substitute the values into the formula.\newlinea10=5×(−5)10−1a_{10} = 5 \times (-5)^{10-1}\newlinea10=5×(−5)9a_{10} = 5 \times (-5)^9
  4. Calculate 1010th term: Calculate the 1010th term.\newlinea10=5×(−5)9a_{10} = 5 \times (-5)^9\newlinea10=5×(−1953125)a_{10} = 5 \times (-1953125)\newlinea10=−9765625a_{10} = -9765625

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