Jami picked three equally spaced integer numbers on the number line. The sum of the first and the second numbers is 40, while the sum of the second and third numbers is 60. What is the largest number ?

A. 15

B. 20

C. 35

D. 45

E. 50

1. 2026 AMC 8 官方解析

设这3个数为$a_1$、$a_2$、$a_3$，

$a_1 + a_2 + a_2 + a_3 = 40 + 60 = 100$ ,

$\because a_1$、$a_2$、$a_3$为等差数列，

$\therefore a_1 + a_3 = 2a_2$ ,

$\therefore a_1 + a_2 + a_2 + a_3 = 4a_2 = 100$ ,

$a_2 = 100 \div 4 = 25$ ,

$a_1 = 40 - 25 = 15 \quad a_3 = 60 - 25 = 35$ .