The sum of 2 + 4 + 6 + 8 + .......... + 80 is :

1540

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1640

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1740

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1440

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Solution

The correct option is D $1640$
Given sequence is: $2 + 4 + 6 + . . . . . . . + 80$
Here, $a = 2, d = 4 - 2 = 2,$ $a_{n} = 80$
$a_{n} = a + (n - 1) d$
$\Rightarrow 80 = 2 + (n - 1) 2$
$\Rightarrow 80 = 2 n \Rightarrow n = 40$
$\Rightarrow S_{40} = \frac{40}{2} {2 a + (n - 1) d}$
$= 20 {4 + 78}$
$= 20 \times 82$
$= 1640$

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