Tentukan jumlah dari 100 suku pertama pada deret aritmatika berikut! A. 2+7+12+17+.... B. 6+10+14+18+.... C. 50+45+40+35+.... D. 16+12+8+4+.....

A.
Penyelesaian:
Diket.:
U1 = a = 2
b = U2 - U1 = 7 - 2 = 5
n = 100
Ditanya:
S100 = ....?
Jawab:
cara 1
Un = a + (n - 1)b
U100 = 2 + (100 - 1)5
U100 = 2 + 99 × 5
U100 = 2 + 495
U100 = 497

S100 = n/2 (U1 + Un)
S100 = 100/2 (2 + 497)
S100 = 50 × 499
S100 =24.950

cara2
S100 = n/2 (2a + (n - 1)b)
S100 = 100/2 (2(2) + (100 - 1)5)
S100 = 50 × (4 + 99 × 5)
S100 = 50 × (4 + 495)
S100 = 50 × 499
S100 = 24.950

B.
Penyelesaian:
Diket.:
U1 = a = 6
b = U2 - U1 = 10 - 6 = 4
n = 100
Ditanya:
S100 = ....?
Jawab:
cara 1
Un = a + (n - 1)b
U100 = 6 + (100 - 1)4
U100 = 6 + 99 × 4
U100 = 6 + 396
U100 = 402

S100 = n/2 (U1 + Un)
S100 = 100/2 (6 + 402)
S100 = 50 × 408
S100 = 20.400

cara 2
S100 = n/2 (2a + (n - 1)b)
S100 = 100/2 (2(6) + (100 - 1)4)
S100 = 50 × (12 + 99 × 4)
S100 = 50 × (12 + 396)
S100 = 50 × 408
S100 = 20.400

C.
Penyelesaian:
Diket.:
U1 = a = 50
b = U2 - U1 = 45 - 50 = - 5
n = 100
Ditanya:
S100 = ....?
Jawab:
cara 1
Un = a + (n - 1)b
U100 = 50 + (100 - 1)(- 5)
U100 = 50 + 99 × (- 5)
U100 = 50 + (- 495)
U100 = - 445

S100 = n/2 (U1 + Un)
S100 = 100/2 (50 + (- 445))
S100 = 50 × (- 395)
S100 = - 19.750

cara 2
S100 = n/2 (2a + (n - 1)b)
S100 = 100/2 (2(50) + (100 - 1)(- 5))
S100 = 50 × (100 + 99 × (- 5))
S100 = 50 × (100 + (- 495)
S100 = 50 × (- 395)
S100 = - 19.750

D.
Penyelesaian:
Diket.:
U1 = a = 16
b = U2 - U1 = 12 - 16 = - 4
n = 100
Ditanya:
S100 = ....?
Jawab:
cara 1
Un = a + (n - 100)b
U100 = 16 + (100 - 1)(- 4)
U100 = 16 + 99 × (- 4)
U100 = 16 + (- 396)
U100 = - 380

S100 = n/2 (U1 + Un)
S100 = 100/2 (16 + (-380))
S100 = 50 × (- 364)
S100 = 18.200

cara 2
S100 = n/2 (2a + (n - 1)b)
S100 = 100/2 (2(16) + (100 - 1)(- 4))
S100 = 50 × (32 + 99 × (- 4)
S100 = 50 × (32 + (- 396)
S100 = 50 × (- 364)
S100 = 18.200

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