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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