Question

Descubra quantos múltiplos de 9 existem entre 50 e 500?​

Answer 1

$> \: resolucao \\ \\ \geqslant \: progressao \: \: aritmetica \\ \\ a1 = 54 \\ an = 495 \\ r = 9 \\ \\ = = = = = = = = = = = = = = = \\ \\ an = a1 + (n - 1)r \\ 495 = 54 + (n - 1)9 \\ 495 = 54 + 9n - 9 \\ 495 = 45 + 9n \\ 495 - 45 = 9n \\ 450 = 9n \\ n = \frac{450}{9} \\ n = 50 \\ \\ = = = = = = = = = = = = = = = \\ \\ \\ > soma \: dos \: multiplos \: de \: 9 \\ \\ sn = \frac{(a1 + an)n}{2} \\ \\ sn = \frac{(54 + 495)50}{2} \\ \\ sn = \frac{549 \times 50}{2} \\ \\ sn = 549 \times 25 \\ \\ sn = 13725 \\ \\ \\ \geqslant \leqslant \geqslant \leqslant \geqslant \leqslant \geqslant \leqslant \geqslant \leqslant \geqslant$