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

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Question

(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 $60$.

$264$	$136$	$72$	$40$
$488$	$(a)$	$(b)$	$(c)$

$4$	$5$	$9.75$	$23.5$
$7$	$(a)$	$(b)$	$(c)$	$(d)$	$(e)$

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

Similar Questions

Observe the following table and determine which number will come in place of $(a)$:
$264$ $136$ $72$ $40$
$488$ $(a)$ $(b)$ $(c)$

In the following number series,one of the numbers does not fit into the series. Mark the wrong number in the series.
$35 \quad 118 \quad 280 \quad 600 \quad 1238 \quad 2504 \quad 5036$

Find the next number in the series: $12, 12, 18, 36, 90, 270, ?$

Find the odd one out from the following sequence:
$10, 25, 49, 81, 121$

$4$ $5$ $9.75$ $23.5$
$7$ $(a)$ $(b)$ $(c)$ $(d)$ $(e)$

Which of the following numbers will come in place of $(d)$?

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