0, 5, 18, 43, 84, 145, ? | vedclass

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Question

(D) Let the given series be $0, 5, 18, 43, 84, 145, ?$.Calculate the differences between consecutive terms:$5 - 0 = 5$$18 - 5 = 13$$43 - 18 = 25$$84 -

Vedclass · Accepted Answer

$230$

Vedclass · Answer

(D) Let the given series be $0, 5, 18, 43, 84, 145, ?$.Calculate the differences between consecutive terms:$5 - 0 = 5$$18 - 5 = 13$$43 - 18 = 25$$84 - 43 = 41$$145 - 84 = 61$The differences are $5, 13, 25, 41, 61$.Now,find the second-order differences:$13 - 5 = 8$$25 - 13 = 12$$41 - 25 = 16$$61 - 41 = 20$The second-order differences are $8, 12, 16, 20$,which form an arithmetic progression with a common difference of $4$.The next second-order difference will be $20 + 4 = 24$.Therefore,the next first-order difference will be $61 + 24 = 85$.The next term in the series is $145 + 85 = 230$.

$0, 5, 18, 43, 84, 145, ?$

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