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U₁ = a = 1
b = 3 - 1 = 2
Un = a + (n - 1) x b
99 = 1 + (n - 1) x 2
99 = 1 + 2n - 2
99 = -1 + 2n
100 = 2n
n = 50
Sn = n/2 x (a + Un)
= 50/2 x (1 + 99)
= 25 x 100
= 2.500
b) 1 - 2 + 3 - 4 + 5 - ... - 100
untuk soal di atas, kita bagi menjadi 2 deret
deret yg 1
1 + 3 + 5 + 7 + ... + 99
U₁ = a = 1 ; b = 3 – 1 = 2 ; n = ?
Un = a + (n - 1) x b ===> 99 = 1 + (n - 1) x 2
99 = 1 + 2n - 2
99 = 2n - 1
100 = 2n ===> n = 50
Sn = n/2 x (a + Un)
= 50/2 x (1 + 99)
= 25 x 100
= 2500
deret yang ke 2
-2 - 4 - 6 - 8 - ... - 100
U₁ = a = -2 ; b = -4 – (-2) = -3 ; n = ?
Un = a + (n - 1) x b ===> -100 = -2 + (n - 1) x (-2)
-100 = -2 - 2n + 2
-100 = -2n =====> n = 50
Sn = n/2 x (a + Un)
= 50/2 x (-2 - 100)
= 25 x (-102)
= -2550
kemudian kita jumlahkan deret yang 1 dan yang 2
===> 2500 - 2550
= -50
Jadi jumlah deret tsb di atas = -50
c) -100 - 99 - 98 - ... + 50
U₁ = a = -100
b = -99 - (-100)
= -99 +100
= 1
Un = a + (n - 1) x b
50 = -100 + (n - 1) x 1
50 = -100 + n - 1
50 = -101 + n
n = 151
Sn = n/2 x (a + Un)
= 151/2 x (-100 + 50)
= 151/2 x (-50)
= -3.775
semoga jelas dan membantu ya