The $100^{\text {th }}$ term of the sequence $1,2,2,3,3,3,4,4$, $4,4, \ldots$ is

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Aicharya · Accepted Answer

$\begin{aligned} & 1^{\text {st }} \text { term } \rightarrow 1,2^{\text {nd }} \text { term }=2,4^{\text {th }} \text { term } \rightarrow 3, \ & 7^{\text {th }} \text { term } \rightarrow 4,11^{\text {th }} \text { term } \rightarrow 5, \ldots \end{aligned}$ Series is $1,2,4,7,11, \ldots$ $a_n=1+\frac{n(n-1)}{2}=\frac{n^2-n+2}{2}$ If $n=14$, then $a_n=92, \mathrm{If} n=15$, then $a_n=106$.

The \(100^{\text {th }}\) term of the sequence \(1,2,2,3,3,3,4,4\), \(4,4, \ldots\) is

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