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Find the 10^th term of the geometric sequence 1,-2,4,dots Answer:

Find the 10th 10^{\text {th }} term of the geometric sequence 1,−2,4,… 1,-2,4, \ldots \newlineAnswer:

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Full solution

Q. Find the 10th 10^{\text {th }} term of the geometric sequence 1,−2,4,… 1,-2,4, \ldots \newlineAnswer:
  1. Identify Sequence Type: Identify the type of sequence. The given sequence alternates signs and each term is twice the absolute value of the previous term, which indicates it is a geometric sequence.
  2. Determine Common Ratio: Determine the common ratio rr of the sequence.\newlineTo find the common ratio, divide the second term by the first term.\newliner=−21=−2r = \frac{-2}{1} = -2
  3. Use Geometric Sequence Formula: Use the formula for the nth term of a geometric sequence.\newlineThe nth term TnT_n of a geometric sequence can be found using the formula Tn=a⋅r(n−1)T_n = a \cdot r^{(n-1)}, where aa is the first term and nn is the term number.
  4. Calculate 1010th Term: Calculate the 1010th term using the formula.\newlineT10=1×(−2)10−1T_{10} = 1 \times (-2)^{10-1}\newlineT10=1×(−2)9T_{10} = 1 \times (-2)^9\newlineT10=1×(−512)T_{10} = 1 \times (-512)\newlineT10=−512T_{10} = -512

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