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

Question

Accepted Answer

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.

Answer

248

Answer

252

Answer

258

Answer

262

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

Explanation

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