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Find the 8^th term of the geometric sequence 5,20,80,dots Answer:

Find the 8th 8^{\text {th }} term of the geometric sequence 5,20,80,… 5,20,80, \ldots \newlineAnswer:

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Full solution

Q. Find the 8th 8^{\text {th }} term of the geometric sequence 5,20,80,… 5,20,80, \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=205=4r = \frac{20}{5} = 4
  3. Use formula for nth term: 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 88th term: Calculate the 88th term using the formula. T8=5×48−1=5×47T_8 = 5 \times 4^{8-1} = 5 \times 4^7
  5. Perform exponentiation: Perform the exponentiation. 47=4×4×4×4×4×4×4=163844^7 = 4 \times 4 \times 4 \times 4 \times 4 \times 4 \times 4 = 16384
  6. Multiply by first term: Multiply the result by the first term.\newlineT8=5×16384=81920T_8 = 5 \times 16384 = 81920

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