What will come in place of the question mark $(?)$ in each of the following number series?
$3$ $4$ $12$ $?$ $196$

45

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40

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41

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49

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None of these

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Solution

The correct option is A $45$
If we observe a pattern,
$3 \times 1 + 1 ² = 3 + 1 = 4$
$4 \times 2 + 2 ² = 8 + 4 = 12$
$12 \times 3 + 3 ² = 36 + 9 = 45$
$45 \times 4 + 4 ² = 180 + 16 = 196$

The ? Will be replaced by $45$
Option A will be the correct answer.

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