Question

1. Find three consecutive interferes whose sum is -30. (Answer choices) A.)-8, -10, -12 B). -11, -12, -13 C.) 11, -10, -9 D.) -8, -9, -10

Find three consecutive even internet’s whose sum is 120
A.) 38, 39, 40
B.) 39, 40, 41
C.) 36, 38, 40
D.) 38, 40 , 42
HELP ASAP

Answer 1

] The three consecutive even numbers are 38, 40 and 42. The smallest of the three is clearly 38. Explanation:Even numbers are of the form [math]2k[/math], [math] k \in \mathbb{Z}[/math]. Three consecutive even numbers are of the form [math]2k[/math], [math]2(k+1)[/math], [math]2(k+2)[/math]. We have that their sum is 120 therefore [math]\\2k + 2(k+1) + 2(k+2) = 120 \Leftrightarrow k+(k+1)+(k+2) = 60 \Leftrightarrow 3(k+1) = 60 \\ \Leftrightarrow k+1=20 \Leftrightarrow \boxed{k=19}.[/math