Question

Considere a soma dos n primeiros termos da PA (47,41,35...) qual é o menor valor de novo para que essa soma seja negativa?

Answer 1

$\boxed{\mathsf{r = a_{n} - a_{(n -1)} }}$

41 -47

-6

$\boxed{ \mathsf{a_{n} = a_{m} + (n -m) \cdot r}}$

47 + (n -1) * (-6)

47 + 6 -6n

53 -6n

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

$S_{n} = \frac{[47 + (53 -6n)] * n}{2}$

$0 > \frac{[100 -6n] * n}{2}$

0 > 100 -6n

n > 100/6

n > 16,67 ∴ 17

$\boxed{\underline{\mathbf{R} \mathsf{esposta \to 17 }}}$