16, 22, 40, 78, 144, ? | vedclass

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(D) The given series is $16, 22, 40, 78, 144, ?$.Let us find the differences between consecutive terms:$22 - 16 = 6$$40 - 22 = 18$$78 - 40 = 38$$144 -

Vedclass · Accepted Answer

$246$

Vedclass · Answer

(D) The given series is $16, 22, 40, 78, 144, ?$.Let us find the differences between consecutive terms:$22 - 16 = 6$$40 - 22 = 18$$78 - 40 = 38$$144 - 78 = 66$Now,let us find the differences of these differences (second-order differences):$18 - 6 = 12$$38 - 18 = 20$$66 - 38 = 28$The differences of the second-order differences are increasing by $8$ ($20 - 12 = 8$,$28 - 20 = 8$).Following this pattern,the next difference in the second-order sequence should be $28 + 8 = 36$.Adding this to the last first-order difference: $66 + 36 = 102$.Finally,adding this to the last term of the series: $144 + 102 = 246$.Therefore,the next term is $246$.

$16, 22, 40, 78, 144, ?$

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