Find the sum of first $20$ terms of the series $4 + 7 + 10 + . . . .$

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Solution

$4 + 7 + 10 + . . . . .$
$a = 4, d = 7 - 4$ $= 3 S_{20} = ?$
$S_{n} = \frac{n}{2} [2 a + (n - 1) d]$

$S_{20} = \frac{20}{2} [2 \times 4 + (20 - 1) 3]$
$= 10 [8 + 57]$
$= 10 \times 65$
$S_{20} = 650$
Sum of the first $20$ terms of the series $= 650$

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