Find the odd term out of the series 888, 440, 216, 104, 48, 22, 6.

Introduction / Context:

This question presents a strictly decreasing number series and asks you to find the odd term out. The odd term is the one that does not obey the rule followed by the others. Such problems assess the ability to detect a uniform pattern and then identify the single value that breaks it.

Given Data / Assumptions:

• The series is 888, 440, 216, 104, 48, 22, 6.
• Exactly one term is inconsistent with the pattern used for the rest.
• Since the sequence decreases smoothly at first, subtraction or division likely plays an important role.
• We must detect a simple rule that works for most terms and see where it fails.

Concept / Approach:

One promising approach is to see if each term is derived from the previous one by halving and then subtracting a fixed number. If that pattern holds through several steps but breaks at one place, the number at that place is the odd term. For this series, halving and subtracting 4 gives a very clean pattern for most transitions, which we can verify step by step.

Step-by-Step Solution:

Step 1: From 888 to 440: half of 888 is 444, and 444 minus 4 equals 440. Step 2: From 440 to 216: half of 440 is 220, and 220 minus 4 equals 216. Step 3: From 216 to 104: half of 216 is 108, and 108 minus 4 equals 104. Step 4: From 104 to 48: half of 104 is 52, and 52 minus 4 equals 48. Step 5: From 48 to the next number, if the same rule continues, we expect half of 48 to be 24, and 24 minus 4 equals 20. Then from 20 we expect half of 20 to be 10, and 10 minus 4 equals 6. However, the given series has 22 instead of 20 before 6, so 22 breaks the pattern.

Verification / Alternative check:

If we reconstruct the ideal series using the rule (next term) = (previous term / 2) - 4, we obtain: 888, 440, 216, 104, 48, 20, 6. Every transition fits the same rule with no exceptions. Comparing this intended sequence with the given one, we see that only the fifth transition differs, where 22 appears instead of 20. The last term 6 is still reachable naturally from 20 by half and minus 4, reinforcing that 22 is the only value inconsistent with the underlying pattern.

Why Other Options Are Wrong:

Term 440 matches the rule from 888 and to 216. Term 216 fits the rule both from 440 and to 104. Term 104 is correctly obtained from 216 and leads correctly to 48. Term 48 is correctly derived from 104 by the rule. All these terms show correct application of the same operation. Only 22 cannot be obtained from 48 by halving and subtracting 4, and it also does not lead to 6 via this rule, making it the unique outlier.

Common Pitfalls:

Students sometimes compute only simple differences between terms and get lost in a non uniform pattern. Others may assume the rule changes mid series rather than looking for one consistent rule that works for almost all terms. Another mistake is to not check the last two transitions carefully, assuming the error must be earlier. However, in many questions the wrong term is placed near the end. Careful verification of every step using the same rule helps to confidently identify the odd term.

Final Answer:

The number that does not satisfy the consistent rule of halving and subtracting 4 is 22, so 22 is the odd term out.