0, 4, 18, 48, ?, 180 | vedclass

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Question

(D) The given series is $0, 4, 18, 48, ?, 180$.We can observe the pattern by finding the differences between consecutive terms:$4 - 0 = 4$$18 - 4 = 14

Vedclass · Accepted Answer

$100$

Vedclass · Answer

(D) The given series is $0, 4, 18, 48, ?, 180$.We can observe the pattern by finding the differences between consecutive terms:$4 - 0 = 4$$18 - 4 = 14$$48 - 18 = 30$The differences are $4, 14, 30, ...$Now,find the second-level differences:$14 - 4 = 10$$30 - 14 = 16$The difference between these is $16 - 10 = 6$.Following this pattern,the next second-level difference should be $16 + 6 = 22$.So,the next first-level difference should be $30 + 22 = 52$.Therefore,the missing term is $48 + 52 = 100$.Alternatively,the series follows the pattern $n^2(n-1)$ for $n = 1, 2, 3, 4, 5, 6$:For $n=1: 1^2(0) = 0$For $n=2: 2^2(1) = 4$For $n=3: 3^2(2) = 18$For $n=4: 4^2(3) = 48$For $n=5: 5^2(4) = 100$For $n=6: 6^2(5) = 180$Thus,the missing term is $100$.

$0, 4, 18, 48, ?, 180$

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