Question

A soma de todos os números inteiros entre 50 e 350 que terminam em 3 é:? me ajudeeem por favor!

Answer 1

$P.A\ (53,63,73,83,...,343)\\\\a_1=53\\a_2=63\\\\r=a_2-a_1\\r=63-53\\r=10\\\\a_n=343\\\\n=?\\\\a_n=a_1+(n-1)\cdot(r)\\343=53+(n-1)\cdot10\\343-53=10n-10\\290=10n-10\\10n=300\\n=30\\\\S_n= \dfrac{(a_1+a_{n})\cdot{n}}{2}\\\\\\Sn= \dfrac{(53+343)\cdot30}{2}\\\\\\S_n=396\cdot15\\\\\boxed{S_n=5940}$

Answer 2

An =A1 + ( n - 1 ) * R
343 = 53 + ( n -1 )* 10
343 = 53 + ( 10n - 10 )
343 = 53 + 10n - 10
10n + 53 - 10 = 343
10n + 43 = 343
10n = 343 - 43
10n = 300
n = 300 / 10
n = 30

Sn = ( A1 + An) * n / 2
Sn = ( 53 + 343 ) *30 / 2
Sn = 396 * 15
Sn = 5940