The next number of the sequence 0, 3, 8, 15, | vedclass

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Question

(C) The given sequence is $0, 3, 8, 15, 24, 35, \ldots$Observe the differences between consecutive terms:$3 - 0 = 3$$8 - 3 = 5$$15 - 8 = 7$$24 - 15 =

Vedclass · Accepted Answer

$48$

Vedclass · Answer

(C) The given sequence is $0, 3, 8, 15, 24, 35, \ldots$Observe the differences between consecutive terms:$3 - 0 = 3$$8 - 3 = 5$$15 - 8 = 7$$24 - 15 = 9$$35 - 24 = 11$The differences are consecutive odd numbers: $3, 5, 7, 9, 11, \ldots$The next difference should be $13$.Therefore,the next term is $35 + 13 = 48$.Alternatively,the sequence follows the pattern $n^2 - 1$ for $n = 1, 2, 3, \ldots$:$1^2 - 1 = 0$$2^2 - 1 = 3$$3^2 - 1 = 8$$4^2 - 1 = 15$$5^2 - 1 = 24$$6^2 - 1 = 35$$7^2 - 1 = 48$Thus,the next number is $48$.

The next number of the sequence $0, 3, 8, 15, 24, 35, \ldots$ is

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