What is the value of 'X' in the sequence 2, 7, 22, 67, 202, X, 1822 ?
- (a) 603
- (b) 605
- (c) 607 ✓ UPSC's answer
- (d) 608
Why the answer is (c)
• Observe the relationship between consecutive terms: each term is obtained by multiplying the previous term by 3 and adding 1.
• Verify with the first step: 2 × 3 + 1 = 7.
• Verify with the second step: 7 × 3 + 1 = 22.
• Verify with the third step: 22 × 3 + 1 = 67.
• Verify with the fourth step: 67 × 3 + 1 = 202.
• Apply the rule to find X: 202 × 3 + 1 = 606 + 1 = 607.
• Confirm the next term: 607 × 3 + 1 = 1821 + 1 = 1822, which matches the sequence, so X is 607.
Why the other options are wrong
- (a) 603
- 603 is incorrect because 202 × 3 + 1 equals 607, not 603.
- (b) 605
- 605 is incorrect because 202 × 3 + 1 equals 607, not 605.
- (d) 608
- 608 is incorrect because 202 × 3 + 1 equals 607, not 608.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2021, held on 10 October 2021. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.