Question

3, 4, 12, 45, ? 1005​

Answer 1

(3*1)+1^2=4

(4*2)+2^2=12

(12*3)+3^2=45

(45*4)+4^2=196

(196*5)+5^2=1005

196 will come in place of ?

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Answer 2

Given:

The given series is 3, 4, 12, 45,? 1005.

To find:

We have to find the missing term.

Solution:

The series is 3, 4, 12, 45,? 1005.

This series follows a specific pattern.

If we multiple consecutive numbers and add the square of that number we will get the next number as follows-

$3 \times 1 + {1}^{2} = 4 \\ 4 \times 2 + {2}^{2} = 12 \\ 12 \times 3 + {3}^{2} = 45$

Thus, the next term will be the fourth multiple of 45 added to the square of 4.

$45 \times 4 + {4}^{2} \\ 180 + 16 \\ = 196$

Thus, the missing term is 196.