Find the missing term in the series below : 6561, 2187, 729, ?, 81, 27

Concept

A geometric sequence has a constant ratio between every pair of consecutive terms. When each term is obtained by dividing the previous term by the same number, that divisor determines the next term.

Application

1. Compute the ratio for the first pair: 6561 ÷ 2187 = 3.

2. Confirm it for the next pair: 2187 ÷ 729 = 3.

3. Apply the same division to the missing position: 729 ÷ 3 = 243.

4. Continue from the missing term: 243 ÷ 3 = 81 and 81 ÷ 3 = 27.

Cross-check

Reading backward, multiplying each term by 3 gives 27 × 3 = 81, 81 × 3 = 243, and 243 × 3 = 729. Therefore, the missing term is 243.