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13,29,427,881,16243\frac{1}{3}, \frac{2}{9}, \frac{4}{27}, \frac{8}{81}, \frac{16}{243}

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Full solution

Q. 13,29,427,881,16243\frac{1}{3}, \frac{2}{9}, \frac{4}{27}, \frac{8}{81}, \frac{16}{243}
  1. Identify Pattern: Identify the pattern in the series 13,29,427,881,16243\frac{1}{3}, \frac{2}{9}, \frac{4}{27}, \frac{8}{81}, \frac{16}{243}. Each term is obtained by multiplying the previous term by 23\frac{2}{3}.
  2. Check Number of Terms: Check if the series has a finite number of terms. The series has 55 terms listed, which is a finite number.
  3. Determine Series Type: Determine if the series is arithmetic or geometric. The ratio between consecutive terms is constant 23\frac{2}{3}, so it's a geometric series.

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