Direction: In the following number series only one number is wrong. Find out the wrong number. 94. What will be come in place of question mark in the given series. 264 262 271 243 308 $x$

### Concept & Logic Identify the pattern of differences between consecutive terms, paying attention to both magnitude and sign. ### Step-by-Step Solution 1. Calculate the differences between consecutive terms: $262 - 264 = -2$ $271 - 262 = +9$ $243 - 271 = -28$ $308 - 243 = +65$ 2. Analyze the magnitudes of these differences: $2, 9, 28, 65$. 3. Relate these magnitudes to perfect cubes: $1^3 + 1 = 1 + 1 = 2$ $2^3 + 1 = 8 + 1 = 9$ $3^3 + 1 = 27 + 1 = 28$ $4^3 + 1 = 64 + 1 = 65$ 4. The pattern for differences is $n^3 + 1$, with alternating signs (negative, positive, negative, positive). 5. The next difference magnitude should be $5^3 + 1 = 125 + 1 = 126$. 6. Following the alternating sign pattern, the next operation should be subtraction ($-126$). 7. Calculate the missing term: $308 - 126 = 182$. ### Exam Strategy & Shortcut When differences grow rapidly (e.g., $2 \rightarrow 9 \rightarrow 28 \rightarrow 65$), immediately check for squares or cubes. Spotting that $28$ is near $27$ ($3^3$) and $65$ is near $64$ ($4^3$) cracks the pattern in seconds. ### Common Pitfall Ignoring the alternating signs. If you just add $126$ to $308$, you get $434$, which is incorrect (and not in the options). ### Final Answer Therefore, the correct answer is **182**.