Question

Tentukan unsur unsur yg dtnyakan pda barisan aritmatika tersebut :
a.)a = 5 dan b = 3
U9 =... dan S10 = ...

b.)b = 17 dan U21 = 336
a = .. dan S8 =...

c.) a = 21 dan b = -8
Un = -99 dan n = ... : Sn=...

d.) a = 2.b + 9. dan n = 15
Un = ... dan Sn = ...

e.) a = 4.Un = -22 dan Sn = -99
b = ....

Answer 1

Un = a + (n-1)b
U9 = 5 + (9-1)3
U9 = 5 + 24
U9 = 29

Sn = n/2 (2a + (n-1)b)
S10 = 10/2 (2(5) + (10-1)3)
S10 = 5 (10 +27)
S10 = 185

b. b=17, U21 = 336
a= ?
S8= ?

U21 = a + (21-1) 17
336 = a + 360
a = 336-360 = -24
S8 = 8/2 (2(-24) + (8-1) 17)
S8 = 4 (-48 + 153)
S8 = 4 (105)
S8 = 420

c.a = 21 , b=-8, Un  = -99
n = ?
Sn = ?
-99 = 21 + (n-1)-8
-99 = 21 - 8n + 8
-99 -21 -8 = -8n
-8n = -128
n = 16
Sn = 16/2 (2(21) + (16-1)(-8))
Sn = 8 (42 + (-120))
Sn = 8 (-78)
Sn = -624

d. a = 2 , b=9 n =15
Un = ?
Sn = ?
U15 = 2 + (15-1)9
U15 = 2 + 126
U15 = 128
S15 = 15/2 (2(2) + (15-1) 9)
S15 = 15/2 (4 +126)
S15 = 15/2 (130)
S15 = 975

e.a = 4, Un = -22 , Sn = -99
b=  ?
Un = 4 + (n-1)b
-22 = 4 + (n-1)b
-26/n-1 = b
Sn = n/2 (2(4) + (n-1)b)
-99 = n/2 (8 + (n-1)(-26/n-1))
-99 = n/2 (8 -26)
-99 = n/2 (-18)
-9n = -99
n = 11

-26/11-1 = b
b = -26/10
b = -2,6