Fill in the blank space for the given series | vedclass

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Question

(B) The pattern of the series is based on the addition of consecutive integers.The differences between consecutive terms are:$6 - 5 = 1$$9 - 6 = 3$$15

Vedclass · Accepted Answer

$25$

Vedclass · Answer

(B) The pattern of the series is based on the addition of consecutive integers.The differences between consecutive terms are:$6 - 5 = 1$$9 - 6 = 3$$15 - 9 = 6$The differences are $1, 3, 6, \ldots$,which follow the pattern of triangular numbers or the sum of consecutive integers: $1, (1+2), (1+2+3), \ldots$Following this logic,the next difference should be $(1+2+3+4) = 10$.Therefore,the missing number is $15 + 10 = 25$.To verify,the next difference should be $(1+2+3+4+5) = 15$,and $25 + 15 = 40$,which matches the final term in the series.

Fill in the blank space for the given series with the correct alternative.
$5, 6, 9, 15, (\ldots), 40$

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Fill in the blank space for the given series with the correct alternative.$5, 6, 9, 15, (\ldots), 40$