Question

Qual é a soma dos números ímpares entre 100 e 1000?

Answer 1

$a_{n} = a_{1} + (n-1)r$

$a_{1} = 101$

$a_{n} = 999$

$r = 2$

$999 = 101 + (n - 1)2\\999 - 101 = 2n - 2\\999 - 101 + 2 = 2n\\900 = 2n\\n = 450$

$S_{n} = \frac{(a_{1} + a_{n} )n}{2}$

$S_{n} = \frac{(101 + 999)450}{2} \\S_{n} = (1100)225\\S_{n} = 247500$