The n^{th} term of the series 2 + 4 + 7 + 11 | vedclass

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(C) Let the $n^{th}$ term be $T_n$. The series is $2, 4, 7, 11, \dots$The differences between consecutive terms are $2, 3, 4, \dots$,which form an Ari

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$\frac{n^2 + n + 2}{2}$

Vedclass · Answer

(C) Let the $n^{th}$ term be $T_n$. The series is $2, 4, 7, 11, \dots$The differences between consecutive terms are $2, 3, 4, \dots$,which form an Arithmetic Progression.Thus,$T_n = T_1 + \sum_{k=1}^{n-1} (k+1)$$T_n = 2 + [2 + 3 + 4 + \dots + n]$$T_n = 1 + [1 + 2 + 3 + \dots + n]$Using the sum formula $\sum_{k=1}^{n} k = \frac{n(n+1)}{2}$,we get:$T_n = 1 + \frac{n(n+1)}{2}$$T_n = \frac{2 + n^2 + n}{2} = \frac{n^2 + n + 2}{2}$.

The $n^{th}$ term of the series $2 + 4 + 7 + 11 + \dots$ is

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