0, 3, 12, 30, ?, 105, 168 | vedclass

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(C) The given series is $0, 3, 12, 30, ?, 105, 168$.Let us find the differences between consecutive terms:$3 - 0 = 3$$12 - 3 = 9$$30 - 12 = 18$Let the

Vedclass · Accepted Answer

$60$

Vedclass · Answer

(C) The given series is $0, 3, 12, 30, ?, 105, 168$.Let us find the differences between consecutive terms:$3 - 0 = 3$$12 - 3 = 9$$30 - 12 = 18$Let the missing term be $x$. The differences are $3, 9, 18, (x - 30), (105 - x), (168 - 105 = 63)$.Now,let us look at the second-order differences:$9 - 3 = 6$$18 - 9 = 9$If the pattern of second-order differences follows an arithmetic progression with a common difference of $3$,the next differences should be $12, 15, 18$.So,$(x - 30) - 18 = 12 \implies x - 30 = 30 \implies x = 60$.Checking the next term: $(105 - 60) = 45$. The difference between $45$ and $30$ is $15$,which fits the pattern.Checking the final term: $(168 - 105) = 63$. The difference between $63$ and $45$ is $18$,which fits the pattern.Therefore,the missing number is $60$.

$0, 3, 12, 30, ?, 105, 168$

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