121,225,361,___
-
442
-
468
-
529
-
564
These are perfect squares: 121=11², 225=15², 361=19². The bases 11, 15, 19 increase by 4 each time. The next base is 23, and 23²=529.
To find the missing number in the sequence 121, 225, 361, ___, we need to identify the pattern or rule governing the sequence.
Let's find the difference between consecutive terms:
225 - 121 = 104 361 - 225 = 136
The differences between consecutive terms are not consistent. However, if we consider the differences between consecutive differences, we can observe a pattern:
136 - 104 = 32
The difference between the differences is constant. Therefore, we can assume that the pattern for this sequence is a quadratic pattern.
To find the missing number, we need to apply the quadratic pattern to the last given term, 361.
Adding the next difference of 32 to 361, we get:
361 + 32 = 393
Therefore, the missing number in the sequence is 393.
Now let's go through the options to see which one matches our answer:
A) 442 - This option is incorrect because it does not follow the pattern of the sequence. B) 468 - This option is incorrect because it does not follow the pattern of the sequence. C) 529 - This option is incorrect because it does not follow the pattern of the sequence. D) 564 - This option is incorrect because it does not follow the pattern of the sequence.
So, the correct answer is C) 529.