Class 10 Math All topics Arithmetic Progressions

Find the sum of $2,4,6,8,,,........2n$

(a)

$n(n+1)$

(b)

$n_{2}$

(c)

$n(n−1)$

(d)

$n_{2}+n$

Correct answer: (a)

Solution: The given sequence is $2,4,6,8,.....2n$

$∴a=2,d=2$ & $a_{k}=2n$

$∴2n=a+(k−1)d$

$⇒2n=2+(k−1)2$

$⇒k=n$

Sum of $n$ terms $=2k (2a+(k−1)d)$

$=2n ×[2(2)+(n−1)(2)]$

$=n(n+1)$

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