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Find the 8^th term of the geometric sequence 2,6,18,dots Answer:

Find the 8th 8^{\text {th }} term of the geometric sequence 2,6,18,… 2,6,18, \ldots \newlineAnswer:

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Full solution

Q. Find the 8th 8^{\text {th }} term of the geometric sequence 2,6,18,… 2,6,18, \ldots \newlineAnswer:
  1. Identify type of sequence: Identify the type of sequence.\newlineThe given sequence is geometric because each term after the first is found by multiplying the previous term by a constant 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=62=3r = \frac{6}{2} = 3
  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 \times r^{(n-1)}, where a1a_1 is the first term and rr is the common ratio.
  4. Calculate 88th term: Calculate the 88th term using the formula. a8=2×38−1=2×37a_8 = 2 \times 3^{8-1} = 2 \times 3^7
  5. Perform exponentiation: Perform the exponentiation. 37=3×3×3×3×3×3×3=21873^7 = 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 = 2187
  6. Multiply by first term: Multiply the result by the first term.\newlinea8=2×2187=4374a_8 = 2 \times 2187 = 4374

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