Question

1) Determine a soma dos 40 primeiros termos da P.A.(8, 2,...).

Answer 1

$r = 2 - 8 = -6\\a_1 = 8\\n = 40\\\\a_n = a_1 + (n-1)r\\a_{40} = 8 + (40-1)(-6)\\a_{40} = 8 + 39 \cdot (-6)\\a_{40} = 8 - 234\\a_{40} = -226\\\\S_{n} = \frac{(a_1 + a_n)n}{2}\\S_{40} = \frac{(8 - 226) \cdot 40}{2}\\S_{40} = -218 \cdot 20\\\boxed{S_{40} = -4360}$