अनुक्रम 2, 12, 36, 80, 150, X में X का मान क्या है?
सही उत्तर: 252
अनुक्रम 2, 12, 36, 80, 150, X का पैटर्न n की घात 3 + n की घात 2 (n^3 + n^2) पर आधारित है। n = 1 के लिए 2, n = 2 के लिए 12, n = 3 के लिए 36, n = 4 के लिए 80, n = 5 के लिए 150 है। इसी प्रकार n = 6 के लिए 6^3 + 6^2 = 216 + 36 = 252 होगा। अतः X = 252 है।
In English (Question & Model Answer)
What is the value of X in the sequence 2, 12, 36, 80, 150, X?
Correct Option: 252
Analyze the given sequence: 2, 12, 36, 80, 150, X. Let us check differences or cubic patterns. Differences: 12 - 2 = 10, 36 - 12 = 24, 80 - 36 = 44, 150 - 80 = 70. Second differences: 24 - 10 = 14, 44 - 24 = 20, 70 - 44 = 26. Third differences: 20 - 14 = 6, 26 - 20 = 6. Since the third difference is constant (6), this is a cubic sequence. Let's check cubic formula n^3 + n^2: For n = 1: 1^3 + 1^2 = 2. For n = 2: 2^3 + 2^2 = 8 + 4 = 12. For n = 3: 3^3 + 3^2 = 27 + 9 = 36. For n = 4: 4^3 + 4^2 = 64 + 16 = 80. For n = 5: 5^3 + 5^2 = 125 + 25 = 150. For n = 6: 6^3 + 6^2 = 216 + 36 = 252. Therefore, X = 252.