अनुक्रम 2, 7, 22, 67, 202, X, 1822 में 'X' का मान क्या है ?
सही उत्तर: (b) 605
दिए गए अनुक्रम 2, 7, 22, 67, 202, X, 1822 में पैटर्न का परीक्षण करते हैं: 2 × 3 + 1 = 7, 7 × 3 + 1 = 22, 22 × 3 + 1 = 67, 67 × 3 + 1 = 202। इस प्रकार प्रत्येक पद में 3 से गुणा करके 1 जोड़ा गया है। X का मान ज्ञात करने के लिए: 202 × 3 + 1 = 606 + 1 = 607। इसकी पुष्टि अगले पद से होती है: 607 × 3 + 1 = 1822। अतः X का मान 607 है, जो विकल्प (c) है।
In English (Question & Model Answer)
What is the value of 'X' in the sequence 2, 7, 22, 67, 202, X, 1822?
Correct Option: (b) 605
Let us find the pattern in the given sequence: 2, 7, 22, 67, 202, X, 1822. Let us calculate the differences or multiplicative relations between consecutive terms: 2 to 7: 2 × 3 + 1 = 7. 7 to 22: 7 × 3 + 1 = 22. 22 to 67: 22 × 3 + 1 = 67. 67 to 202: 67 × 3 + 1 = 201 + 1 = 202. The underlying mathematical pattern is multiply by 3 and add 1 (Tn = 3(Tn-1) + 1). Applying this exact rule to find X: X = 202 × 3 + 1 = 606 + 1 = 607? Wait, let's recalculate: 202 × 3 = 606, 606 + 1 = 607. Wait, let's check the next term with X = 607: 607 × 3 + 1 = 1821 + 1 = 1822. This matches the last term 1822 perfectly! Therefore, X = 607. Wait, let's check the options: (a) 603, (b) 605, (c) 607, (d) 608. Since X = 607, it corresponds to option (c).