The first term of the {11^{th}} group in the | vedclass

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(C) The number of elements in the $n^{th}$ group is given by $(2n - 1)$.The first term of the $n^{th}$ group is the sum of the number of elements in a

Vedclass · Accepted Answer

$101$

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(C) The number of elements in the $n^{th}$ group is given by $(2n - 1)$.The first term of the $n^{th}$ group is the sum of the number of elements in all previous $(n-1)$ groups plus $1$.The number of elements in the first $(n-1)$ groups is $\sum_{k=1}^{n-1} (2k - 1) = (n-1)^2$.Therefore,the first term of the $n^{th}$ group is $(n-1)^2 + 1$.For the $11^{th}$ group,$n = 11$.First term $= (11 - 1)^2 + 1 = 10^2 + 1 = 100 + 1 = 101$.

The first term of the ${11^{th}}$ group in the following sequence of groups $(1), (2, 3, 4), (5, 6, 7, 8, 9), \dots$ is

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