Find the next term in the series: 0, 2, 3, 5, | vedclass

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Question

(D) The given series is a combination of two alternating series:$(i)$ The first series consists of the terms at odd positions: $0, 3, 8, 15, 24, ?$The

Vedclass · Accepted Answer

$35$

Vedclass · Answer

(D) The given series is a combination of two alternating series:$(i)$ The first series consists of the terms at odd positions: $0, 3, 8, 15, 24, ?$The pattern is: $0 + 3 = 3$$3 + 5 = 8$$8 + 7 = 15$$15 + 9 = 24$Following this pattern of adding consecutive odd numbers $(3, 5, 7, 9, 11)$,the next term is $24 + 11 = 35$.$(ii)$ The second series consists of the terms at even positions: $2, 5, 10, 17, 26$This follows the pattern $(n^2 + 1)$ for $n = 1, 2, 3, 4, 5$ $(1^2+1=2, 2^2+1=5, 3^2+1=10, 4^2+1=17, 5^2+1=26)$.Since the question asks for the term following $26$,which is the $11^{th}$ term,it belongs to the first series. Thus,the answer is $35$.

Find the next term in the series: $0, 2, 3, 5, 8, 10, 15, 17, 24, 26, ?$

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