Choose the most appropriate option to replace (?). 4 200 369 513 634 ? Option 1) 788 Option 2) 715 Option 3) 734 Option 4) 755 Option 5) None of these
Question
Choose the most appropriate option to replace (?).
4 200 369 513 634 ?
Option 1) 788
Option 2) 715
Option 3) 734
Option 4) 755
Option 5) None of these
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Answer
The correct option is C) 734
Analyzing the given series:
$$4, 200, 369, 513, 634, ?$$
We can observe the following pattern in the differences between consecutive terms:
$$200 - 4 = 196$$
$$369 - 200 = 169$$
$$513 - 369 = 144$$
$$634 - 513 = 121$$
The differences (196, 169, 144, 121) are consecutive perfect squares:
$$14^2, 13^2, 12^2, and 11^2$$
Continuing this pattern, the next difference should be:
$$10^2 = 100$$
Thus, adding this difference to the last term in the series, we get:
$$634 + 100 = 734$$
Therefore, 734 is the correct option. This pattern of consecutive perfect squares confirms that option C) 734 is the right choice.
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