1. Tardigrade
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  3. Mathematics
  4. Statement-1: Suppose that Sn denotes the sum to n terms of a sequence. If S1=1, S2=4 and S3=9 then S10=100. Statement-2: Sum of the first n odd natural numbers is n2.

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Q. Statement-1: Suppose that $S_n$ denotes the sum to $n$ terms of a sequence. If $S_1=1, S_2=4$ and $S_3=9$ then $S_{10}=100$.
Statement-2: Sum of the first $n$ odd natural numbers is $n^2$.

Sequences and Series

Solution:

If $S _{ n }=( n -1)( n -2)( n -3)+ n ^2$
$S _1, S _2, S _3$ all are true but $S _{10} \neq 100$ and $S -2$ is obviously true