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In any such series problems, you have to catch the pattern first. Three ways 1. Increasing at a decent rate(may be at a constant rate for easy problems)     Then its a chance of Addition series. 2. Increasing at a drastic rate      Then its a chance of multiplication series. 3. Decreasing       Then its a chance of subtraction or division. 0,18,  ,294,648,1210,2028 It's increasing very drastically.Surely it's a multiplication case. Now we have to see pattern of multiplication. By observation skill(which you have to get by practice) nth term : 2*(n-1)*(2n-1)^2.  when n=3 i.e the 3rd term or the missing term we get   2*(3-1)*(6-1)^2 =2*2*5*5 =100 Answer.  

Answer

The kth term of the series is 2*(k-1)*(2k-1)^2. Hence 3rd term would be 2*(3-1)*(6-1)^2=2*2*5*5=100

Answer

0, 18, __, 294, 648, 1210, 2028

Break the numbers into factors

0, 2*3*3, ____, 2*3*7*7, 2*2*2*3*3*3*3,  2*5*11*11,  2*2*3*13*13

Now we see that in some numbers we have square of odd numbers in series

So we allign them in sqaure of odd numbers and see what we find

0, 2*(3^2), ______, 2*3*(7^2),  2*2*2*(9^2),  2*5*(11^2),   2*2*3*(13^2) 

Now we multiply the remaining number 

 

0,  2*(3^2),  ___,  6*(7^2),  8*(9^2),  10*(11^2),  12*(13^2)

By the series we see that we have to multiply 1^2  with 0

0*(1^2),  2*(3^2),  ___,  6*(7^2),  8*(9^2),  10*(11^2),  12*(13^2)

Here we see that with each Sqaure of odd numbers we have an Even numer

So the blank will have an Even number 4 according to the series and sqaure of odd number 5

So 4*(5^2)  = 100

Now we see that with each Sqaure of odd numbers we have an Even numer 

 

Answer
The kth term of the series is 2*(k-1)*(2k-1)^2. Hence 3rd term would be 2*2*5*5 viz 100.

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