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Find the 10^th term of the geometric sequence 7,28,112,dots Answer:

Find the 10th 10^{\text {th }} term of the geometric sequence 7,28,112,… 7,28,112, \ldots \newlineAnswer:

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Full solution

Q. Find the 10th 10^{\text {th }} term of the geometric sequence 7,28,112,… 7,28,112, \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.
  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.\newline287=4\frac{28}{7} = 4\newlineCommon Ratio rr: 44
  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 1010th term: Calculate the 1010th term using the formula.\newlinea10=7×410−1a_{10} = 7 \times 4^{10-1}\newlinea10=7×49a_{10} = 7 \times 4^9
  5. Perform exponentiation: Perform the exponentiation. 49=2621444^9 = 262144
  6. Multiply by first term: Multiply the result by the first term.\newlinea10=7×262144a_{10} = 7 \times 262144\newlinea10=1835008a_{10} = 1835008

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