UPSC Prelims 2024·CSAT·Logical Reasoning·Series and Sequences

What is the value of X in the sequence 2, 12, 36, 80, 150, X?

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Last updated 23 May 2026, 3:31 pm IST
  1. A248
  2. B252Correct
  3. C258
  4. D262

Explanation

The sequence is 2, 12, 36, 80, 150, X. Let's analyze the pattern by looking at each term in relation to its position 'n': For n=1, the term is 2. We can write this as 1^3 + 1^2 = 1 + 1 = 2. For n=2, the term is 12. We can write this as 2^3 + 2^2 = 8 + 4 = 12. For n=3, the term is 36. We can write this as 3^3 + 3^2 = 27 + 9 = 36. For n=4, the term is 80. We can write this as 4^3 + 4^2 = 64 + 16 = 80. For n=5, the term is 150. We can write this as 5^3 + 5^2 = 125 + 25 = 150. The pattern for the nth term of the sequence is n^3 + n^2. To find X, which is the 6th term (n=6), we apply this pattern: X = 6^3 + 6^2 X = 216 + 36 X = 252 Therefore, the value of X is 252. Analyzing the options: A) 248 - Incorrect. B) 252 - Correct, matches our calculated value. C) 258 - Incorrect. D) 262 - Incorrect. The final answer is B.
Logical Reasoning: What is the value of X in the sequence 2, 12, 36, 80, 150, X?
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