Question

determine a soma dos 50 primeiros termos da P.A
(2,4,6,8...)   e   (3,$\frac{7}{2}$,...)

Answer 1

Sn = (a1+an).n/2
an = a1+(n-1).r
r = a2-a1 = 4-2 = 2
a50 = 2+(50-1).2
a50 = 2+49.2
a50 = 2+98
a50 = 101
Sn = (2+101).50/2
Sn = 202 . 25
Sn = 5050

Answer 2

$P.A (2,4,6,8,...)$

$a_{1}=2$
$a_{2}=4$

$r = a_{2} - a_{1} => 4 - 2 => r = 2$

$a_{50} = a_{1} + 49r$
$a_{50} = 2 + 49*2$
$a_{50} = 2(1 + 49)$
$a_{50} = 2(50)$
$a_{50} = 100$

$S_{n} = (a_{1} + a_{n})*n/2$
$S_{50} = (a_{1} + a_{50})*50/2$
$S_{50} = (2 + 100)*25$
$S_{50} = 102*25$
$S_{50} = 2550$
_______________________

$P.A(3,7/2,...)$

$a_{1} = 3$
$a_{2} = 7/2$

$r = a_{2} - a_{1} => (7/2) - 3 => (7/2) - (6/2) => (7 - 6)/2 => r = 1 / 2$

$a_{50} = a_{1} + 49r$
$a_{50} = 3 + 49*1/2$
$a_{50} = (6/2) + (49/2)$
$a_{50} = (6+49)/2$
$a_{50} = 55/2$

$S_{50} = (a_{1} + a_{50})*50/2$
$S_{50} = (3 + [55/2])*25$
$S_{50} = ([6/2]+[55/2])*25$
$S_{50} = ([6+55]/2)*25$
$S_{50} = (61/2)*25$
$S_{50} = 1525/2$