Find the missing term in the series: 2, 6, 12 | vedclass

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Question

(B) The given series is $2, 6, 12, 20, 30, ?$.Let's analyze the differences between consecutive terms:$6 - 2 = 4$$12 - 6 = 6$$20 - 12 = 8$$30 - 20 = 1

Vedclass · Accepted Answer

$42$

Vedclass · Answer

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

Find the missing term in the series: $2, 6, 12, 20, 30, ?$

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