Fill in the blank space for the given series | vedclass

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Question

(B) The given series is $2, 6, 12, 20, 30, ?$. Observe the differences between consecutive terms: $6 - 2 = 4$ $12 - 6 = 6$ $20 - 12 = 8$ $30 - 20 = 10

Vedclass · Accepted Answer

$42$

Vedclass · Answer

(B) The given series is $2, 6, 12, 20, 30, ?$. Observe the differences between consecutive terms: $6 - 2 = 4$ $12 - 6 = 6$ $20 - 12 = 8$ $30 - 20 = 10$ The differences are $4, 6, 8, 10$,which form an arithmetic progression with a common difference of $2$. The next difference should be $10 + 2 = 12$. Therefore,the next term is $30 + 12 = 42$. Alternatively,the series follows the pattern $n^2 + n$ (or $n(n+1)$): $1^2 + 1 = 2$ $2^2 + 2 = 6$ $3^2 + 3 = 12$ $4^2 + 4 = 20$ $5^2 + 5 = 30$ $6^2 + 6 = 42$ Thus,the correct option is $B$.

Fill in the blank space for the given series with the correct alternative: $2, 6, 12, 20, 30, ?$

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