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Find the 9^th term of the geometric sequence 1,4,16,dots Answer:

Find the 9th 9^{\text {th }} term of the geometric sequence 1,4,16,… 1,4,16, \ldots \newlineAnswer:

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Full solution

Q. Find the 9th 9^{\text {th }} term of the geometric sequence 1,4,16,… 1,4,16, \ldots \newlineAnswer:
  1. Identify Sequence Type: Identify the type of sequence. The given sequence is geometric because each term after the first is found by multiplying the previous term by a constant called the common ratio.
  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=41=4r = \frac{4}{1} = 4
  3. Use Formula for nth Term: 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.
  4. Calculate 99th Term: Calculate the 99th term using the formula.\newlinea9=a1⋅r9−1a_9 = a_1 \cdot r^{9-1}\newlinea9=1⋅49−1a_9 = 1 \cdot 4^{9-1}\newlinea9=1⋅48a_9 = 1 \cdot 4^8
  5. Perform Exponentiation: Perform the exponentiation to find the 9th9^{\text{th}} term.a9=1×65536a_9 = 1 \times 65536a9=65536a_9 = 65536

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