Question

2+4+6+8...+n=600
Halla N

Answer 1

A1 = 2
d = 2
An=?
Sn = 600

An = A1 +(n-1) d
n =(An - A1)/d + 1 (1)

Sn = (A1 +An)/2×n
n = Sn / (A1 +An) /2
n = 2Sn/(A1 +An) (2)

Sistema de ecuaciónes con dos incógnitas
n = n
(An - A1)/d + 1 = 2Sn / (A1 +An)
(An - A1) /d - 2Sn/(A1 +An) = - 1
[(An-A1)(An+A1) - d2Sn] / (d)(An +A1) = - 1
An² - A1² - 2Snd = - (d) (An +A1)
An² - (2)² - 2×600×2 = -2×2 -2An
An² - 4 - 2400 = - 4 - 2An
An² +2An - 2400 = 0
(An - 48) (An+50) = 0
An - 48 = 0
An = 48

An +50 = 0
An = - 50 (se descarta porque es negativa)

Respuesta N = 48