Question

Арифметическая прогрессия:
1)a8=23,a12=35, a3=?
2)a2=5,a3=9,a10=?

Answer 1

1)a8=23,a12=35,
d=(a12-a8)/4=(35-23)/4=3
a1=a8-7d=23-7*3=23-21=2
 a3=a1+2d=2+2*3=8
2)a2=5,a3=9,
d=a3-a2=9-5=4
a1=a2-d=5-4=1
a10=a1+9d=1+9*4=37

Answer 2

1)a8=23,a12=35, a3=?
a8 = a1 + 7*d - система уравнений
a12 = a1 + 11*d
23 = a1 + 7*d
35 = a1 + 11*d ⇒ a1 = 35 - 11*d
23 = 35 -11*d + 7*d
23 - 35 = - 4 *d
-12 = - 4* d (сокращаем минусы)
d = 3
a1 = 35 - 11 *3
a1 = 2
a3 = a1 + 2*d
a3 = 2 + 2*3
a3 = 8