The next number in the finite sequence 486, 324, 216, 144, … is

Concept

In a geometric sequence, every term is obtained by multiplying the preceding term by one constant called the common ratio.

If consecutive-term ratios are equal, the same ratio is applied once more to find the next term.

Application

1. Compare 324 with 486: 324 ÷ 486 = 2/3.

2. Check the next pair: 216 ÷ 324 = 2/3.

3. Check again: 144 ÷ 216 = 2/3. Thus the common ratio remains 2/3.

4. Apply that ratio to the last shown term: 144 × 2/3 = 96.

Cross-check

Working backward gives 96 × 3/2 = 144, which reproduces the preceding term and confirms the same ratio.

Therefore, the next number is 96.