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Arithmetic Progressions — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSArithmetic Progressions1 Mark
Question
Write the sum of first n even natural numbers.
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Answer

We have,
2 + 4 + 6 + ... up to n terms
$\therefore\text{S}_\text{n}=\frac{\text{n}}{2}[2\times2+(\text{n}-1)\times2]$
$=\frac{\text{n}}{2}[4+2\text{n}-2]$
$=\frac{\text{n}}{2}[2\text{n}+2]$
$=\frac{\text{n}}{2}\times2(\text{n}+1)$
$\text{n}(\text{n}+1)$
$\therefore2+4+6+\ ...$ up to n terms = n (n + 1)
Hence, the sum of first n even natural numbers is n (n + 1)

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