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Find the 10^th term of the geometric sequence 9,45,225,dots Answer:

Find the 10th 10^{\text {th }} term of the geometric sequence 9,45,225,… 9,45,225, \ldots \newlineAnswer:

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Full solution

Q. Find the 10th 10^{\text {th }} term of the geometric sequence 9,45,225,… 9,45,225, \ldots \newlineAnswer:
  1. Identify Sequence Type: Identify the type of sequence. The given sequence is geometric because each term after the first is obtained 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=459=5r = \frac{45}{9} = 5
  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 1010th Term: Calculate the 1010th term using the formula.\newlinea10=9×510−1a_{10} = 9 \times 5^{10-1}\newlinea10=9×59a_{10} = 9 \times 5^9
  5. Perform Exponentiation: Perform the exponentiation.\newline59=19531255^9 = 1953125
  6. Multiply by First Term: Multiply the result by the first term.\newlinea10=9×1953125a_{10} = 9 \times 1953125\newlinea10=17578125a_{10} = 17578125

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