Multiple choice

Insert the missing number in the given series : $ 0,4,18,48, ?, 180$

  1. $58$
  2. $68$
  3. $84$
  4. $100$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The series is 0, 4, 18, 48, ?, 180. Differences: 4, 14, 30, ... Second differences: 10, 16, ... This is not immediately obvious. Alternatively: 1^2*0=0, 2^2*1=4, 3^2*2=18, 4^2*3=48, 5^2*4=100, 6^2*5=180.

AI explanation

The series follows the pattern of multiplying the square of natural numbers by increasing integers, expressed by the formula n multiplied by (n squared minus 1). For the first term, 1 times (1 squared minus 1) equals 0; the second term is 2 times (2 squared minus 1) equals 6, which does not match 4. The correct formula is n multiplied by n squared minus n, making the second term 2 times 2 which is 4, and the third term 3 times 6 equals 18. Testing n=5 gives 5 times 20, which equals 100. Therefore, the missing number is 100.

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