tentukan Un dan n dari setiap deret berikut! a.2+4+6+8+....+Un=1892 b.1+3+5+7+....+Un=400 c.9+12+15+18+....+Un=750 d.900+895+890+885+.... +Un=17.050 tolong di

Semua merupakan deret aritmatika

a. 2+4+6+8+....+Un=1892
a = 2
b = +2
Sn = 1892
Sn = n/2 (2a + (n-1)b)
1892 = n/2 (2.2 + (n-1)2)
3784 = n (4 + 2n - 2)
3784 = n (2 + 2n)
3784 = 2n^2 + 2n
1892 = n^2 + n
n^2 + n - 1892 = 0
(n+44)(n-43) = 0
banyak bilangan pasti positif (n>0)
maka n = 43
Un = a + (n-1)b
U43 = 2 + (43-1)2
U43 = 2 + 42.2
U43 = 2 + 84
U43 = 86

b. 1+3+5+7+....+Un=400
a = 1
b = 2
Sn = 400
Sn = n/2 (2a + (n-1)b)
400 = n/2 (2.1 + (n-1)2)
400 = n/2 (2 + 2n - 2)
400 = n/2 (2n)
400 = n^2
n^2 - 400 = 0
(n+20)(n-20) = 0
banyak bilangan pasti positif (n>0)
maka n = 20
Un = a + (n-1)b
U20 = 1 + (20-1)2
U20 = 1 + (19)2
U20 = 1 + 38
U20 = 39

c. 9+12+15+18+....+Un=750
a = 9
b = 3
Sn = 750
Sn = n/2 (2a + (n-1)b)
750 = n/2 (2.9 + (n-1)3)
750 = n/2 (18 + 3n - 3)
750 = n/2 (3n + 15)
500 = n^2 + 5n
n^2 + 5n - 500 = 0
(n+25)(n-20) = 0
banyak bilangan pasti positif (n>0)
maka n = 20
Un = a + (n-1)b
U20 = 9 + (20-1)3
U20 = 9 + (19)3
U20 = 9 + 57
U20 = 66

d. 900+895+890+885+.... +Un=17.050
a = 900
b = -5
Sn = 17050
Sn = n/2 (2a + (n-1)b)
17050 = n/2 (2.900 + (n-1)(-5))
17050 = n/2 (1800 + 5 - 5n)
17050 = n/2 (1805 - 5n)
34100 = n 5(361 - n)
6820 = 361n - n^2
n^2 - 361n + 6820 = 0
(n-20)(n-341) = 0
n = 20 atau n = 341

n = 20
Un = a + (n-1)b
U20 = 900 + (20-1)(-5)
U20 = 900 + (19)(-5)
U20 = 900 - 95
U20 = 805

n = 341
Un = a + (n-1)b
U341 = 900 + (341-1)(-5)
U341 = 900 + (340)(-5)
U341 = 900 - 1700
U341 = -800

Semoga membantu :)