suatu barisan geometri dengan U2=1 dan U6=1/16,maka jumlah 5 suku yg pertama adalah...

Mapel : Matematika
Bab: Barisan dan deret

U2 = a × r = 1
U6 = a × r^5 = 1/16

a × r^5 = 1/16
a × r = 1
___________ ÷

r^4 = 1/16
r = 1/2

a × 1/2 = 1
a = 2

S5 = 2(1 - 1/2^5)/1 - 1/2
S5 = 2(1 - 1/32)/1/2

S5 = 2(31/32)/1/2
S5 = 62/32/1/2

S5 = 62/32 × 2/1
S5 = 124/32
S5 = 3,875
S5 = 3 7/8

U2 = a × r^(2 - 1) = a × r = 1
U6 = a × r^(6 - 1) = a × r^5 = 1/16
→ mencari r
U6/U2 = (a × r^5)/(a × r) = (1/16)/1
r⁴ = 1/16
r = ½
→ mencari a
a × r = 1
a × ½ = 1
a = 2
→ mencari S5
Sn = a(1 - r^n)/(1 - r)
S5 = 2(1 - (½)^5)/(1 - ½)
S5 = 2(1 - 1/32)/(½)
S5 = 2(31/32)/(½)
S5 = 31/8