an=21, n=7, Sn=105 найдите a1 и d

(а1+an) / 2=Sn/n

a1=2Sn/n-an=2*105/7-21=9

an=a1+d (n-1)

d = (an-a1) / (n-1) = (21-9) / 6=2

а7=21 a7 = a1+6d = 21 (1)

S7=105 S7 = (2a1+6d) * 7/2 = 105 (2)

(1) : a1 = 21 - 6d

(2) : (a1+3d) * 7 = 105

Подставим (1) в (2):

(21-6d + 3d) = 105/7

21-3d = 15

3d = 6

d=2

a1 = 21-12=9

Ответ: 9 и 2.