For the following problem, a numerical sequence is provided where a single entry does not fit the established rule. Identify the erroneous value from the sequence.

160, 80, 120, 300, 1055, 4725, 25987.5

The correct answer is 1055.

To find the odd one out, we need to first discover the hidden rule governing the sequence:

The sequence: 160, 80, 120, 300, 1055, 4725, 25987.5

Let's examine the ratio between each consecutive pair of terms:

80 ÷ 160 = 0.5
120 ÷ 80 = 1.5
300 ÷ 120 = 2.5
1055 ÷ 300 ≈ 3.517 ← suspicious!
4725 ÷ 1055 ≈ 4.478 ← also off
25987.5 ÷ 4725 = 5.5

A clear pattern is emerging in the multipliers: 0.5, 1.5, 2.5, 3.5, 4.5, 5.5 — each multiplier increases by 1.0.

Let's verify by applying the correct rule step by step:

Term 1: 160
Term 2: 160 × 0.5 = 80 ✓
Term 3: 80 × 1.5 = 120 ✓
Term 4: 120 × 2.5 = 300 ✓
Term 5: 300 × 3.5 = 1050 — but the sequence shows 1055 ✗
Term 6: 1050 × 4.5 = 4725 ✓ (confirms 1050 was the correct value)
Term 7: 4725 × 5.5 = 25987.5 ✓

The rule is: each term is obtained by multiplying the previous term by the next value in the series (0.5, 1.5, 2.5, 3.5, 4.5, 5.5, …). The 5th term should be 1050, not 1055. Therefore, 1055 is the erroneous value in the sequence.