In the series 7, 8, 18, 57, 228, 1165, 6996, which one number is wrong because it does not follow the clear multiplication-plus pattern followed by the others?

Introduction / Context:
This question involves a non-trivial number series where each term is generated from the previous one using a combination of multiplication and addition. The task is to detect the consistent rule and identify which term breaks that rule. Such questions are slightly more challenging and often appear in higher-level aptitude and reasoning exams.

Given Data / Assumptions:
The series is: 7, 8, 18, 57, 228, 1165, 6996. We assume that all terms except one follow a rule of the form “multiply by an integer and then add the same integer,” with the integer increasing step by step. Exactly one term is incorrect.

Concept / Approach:
A common pattern for such sequences is: next term = current term * n + n, where n increases by 1 at each step (for example, *1 + 1, then *2 + 2, then *3 + 3, and so on). We test whether this rule fits the series and see which term violates it.

Step-by-Step Solution:
Step 1: Start from 7 and check the transitions.7 to 8: 7 * 1 + 1 = 8 (fits the rule with n = 1).8 to 18: 8 * 2 + 2 = 16 + 2 = 18 (fits with n = 2).18 to 57: 18 * 3 + 3 = 54 + 3 = 57 (fits with n = 3).Step 2: Continue the same pattern.The next step should use n = 4: 57 * 4 + 4 = 228 + 4 = 232. Hence, the correct next term should be 232.Step 3: However, the series gives 228 instead of 232. So the term 228 does not follow the *4 + 4 rule.Step 4: Check the following term using the corrected value 232: With n = 5, we get 232 * 5 + 5 = 1160 + 5 = 1165, which matches the given series.Step 5: Finally, with n = 6, we check 1165 * 6 + 6 = 6990 + 6 = 6996, which again matches the given value.

Verification / Alternative check:
If we keep 228 as given, the rule *n + n cannot be applied consistently from one term to the next, because 57 * 4 + 4 is not equal to 228. In contrast, replacing 228 with 232 restores a perfect pattern: *1 + 1, *2 + 2, *3 + 3, *4 + 4, *5 + 5, *6 + 6. Both 1165 and 6996 fit this pattern when 232 is used, so 228 must be the incorrect term.

Why Other Options Are Wrong:
57, 1165 and 6996 all match the rule when the fourth term is correctly taken as 232. Changing any of these would break the clean *n + n pattern across the sequence. Therefore, they cannot be considered the unique wrong term.

Common Pitfalls:
Students may try to guess a simpler multiplication-only pattern or may assume inconsistent operations between different pairs of terms. The key is to notice the gradual increase of the multiplier and the same number being added, which is a common construction in exam series questions.

Final Answer:
The only term that does not follow the “multiply by n and add n” pattern is 228.