UPSC Exam  >  UPSC Questions  >   : 6, 9, 14, 21, 30, ?, 54a)39b)33c)36... Start Learning for Free
नीचे दी गई श्रृंखला में लुप्त संख्या ज्ञात कीजिए: 6, 9, 14, 21, 30, ?, 54
  • a)
    39
  • b)
    33
  • c)
    36
  • d)
    41
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
: 6, 9, 14, 21, 30, ?, 54a)39b)33c)36d)41Correct answer is opt...
Pattern:
To find the missing number in the given sequence, we need to identify a pattern or rule that is followed in the sequence.

Observation:
Looking at the given sequence: 6, 9, 14, 21, 30, ?, 54, we can observe the following pattern:
- The difference between the consecutive terms is increasing by 3 each time.

Explanation:
Let's analyze the given sequence step by step:

1. The difference between the first two terms is 9 - 6 = 3.

2. The difference between the second and third terms is 14 - 9 = 5.

3. The difference between the third and fourth terms is 21 - 14 = 7.

4. The difference between the fourth and fifth terms is 30 - 21 = 9.

5. So, the difference between the fifth and sixth terms should be 9 + 3 = 12.

6. Adding this difference to the last known term, 30 + 12 = 42.

7. However, the given sequence has 54 as the next term, which is not equal to 42.

Correction:
As the given sequence does not follow the observed pattern, we need to consider an alternative pattern.

Alternative Pattern:
Upon closer observation, we can see that the given sequence represents the square of consecutive natural numbers: 2^2, 3^2, 4^2, 5^2, 6^2, ?.

Calculation:
1. The square of 6 is 6^2 = 36.

Conclusion:
Therefore, the missing number in the given sequence is 36. Option C is the correct answer.
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Community Answer
: 6, 9, 14, 21, 30, ?, 54a)39b)33c)36d)41Correct answer is opt...
6+3=9
9+5 = 14
14+7=21
21 +9= 30
30 + 11 = 41 = ?
41 + 13 = 54
इसलिए विकल्प (d) सही उत्तर है।
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