Question

Quantos termos devemos somar na PA (-5, -1, 3...) para que a soma seja 1590.

Answer 1

a1 = -5
a2 = -1
r = -1 - ( -5)  = -1 + 5 = 4 ****

an = -5 + ( n - 1)4
an = -5 + 4n - 4
an = 4n - 9  ****

1590 = [- 5 + (4n - 9 ] * n//2
1590/1= ( 4n - 14) * n/2
(4n² - 14n )/2 = 1590/1
4n² - 14n = 2 ( 1590)
4n² - 14n = 3180
2n² - 7n  - 1590 = 0
delta = 49 + 12720 =12769 = +V12769 =  + 113
n = ( 7 + 113 )/4
n1 =  120/4 =  30 ****