CBSE BoardEnglish MediumSTD 11 ScienceMathsArithmetic Progressions1 Mark
Question
Write the sum of first n odd natural numbers.
✓
Answer
We have,
$1 + 3 + 5 + ...$ up to n terms
$\therefore\text{S}_\text{n}=\frac{\text{n}}{2}[2\times1+(\text{n}-1)\times2]$
$=\frac{\text{n}}{2}[2+2\text{n}-2]$
$=\frac{\text{n}}{2}\times2\text{n}$
$=\text{n}^2$
$\therefore1+3+5+\ ...$ up to n terms $= n^2$
Hence, sum of first n odd natural numbers is $n^2$.
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