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Kelas : IX SMP
Bab : Barisan dan deret
Pembahasan :
1 - 2 + 3 - 4 + ... - 100
= -1 - 1 - 1 - 1 - ... - 1
= -(1 + 1 + ... + 1)
= -(100/2)
= -50
————————————————
Un = 50
a + (n - 1)b = 50
-100 + n - 1 = 50
n - 101 = 50
n = 151
-100 - 99 - 98 - ... + 50
= S151
= 151/2(-100 + 50)
= 151/2(-50)
= -3775
a.)
1-2+3-4+5-6....99-100 =
(1-2)+(3-4)+(5-6)+......(99-100) =
-1+(-1)+(-1)......-1 =
-(50) =
-50
b.)
-100-99-98-...-2-1-0+1+2+...+48+49+50 =
-50-49-48-47-......-0+1+2+......+50 = 0
jadi, tersisa -100-99-......-52-51
-99-51 = -150
-98-52 = -150
.
.
.
-76-74 = -150
hanya -75yang tidak memiliki pasangan
dari -99 ==> -76 = 24
jadi, hasilnya adalah
(24×-150) - 75 -100 =
-3600 - 175 =
-3775