jumlah bilangan kelipatan 7 antara 100 dan 300 adalah

Diketahui:
Deret aritmatika
a = 105
b = 7
Un = 294

Ditanyakan:
Sn

Jawab:
Cari banyak bilangan (n)
Un = 294
a + (n-1)b = 294
105 + (n-1) 7 = 294
(n-1) 7 = 294 - 105
7n - 7 = 189
7n = 189 + 7
7n = 196
n = 28
Ada 28 bilangan berkelipatan 7 antara 100 dan 300

Cari jumlah ke-28 bilangan tersebut
Sn = n/2 (a + Un)
Sn = 28/2 (105 + 294)
Sn = 14 (399)
Sn = 5.586

105,112,119,126,133,140,147,154,161,168,175,182,189,196,203,210,217,224,231,238,245,252,259,266,273,280,287,294

a = 105
b = 7
Un = 294

Un = a + (n - 1) × b
294 = 105 + (n - 1) × 7
294 - 105 = 7n - 7
189 = 7n - 7
7n = 189 + 7
7n = 196
n = 196/7
n = 28


Sn = 1/2(n) [2a + (n - 1) × b]
S28 = 1/2(28) [2(105) + (28 - 1) × 7]
S28 = 14 [210 + 27(7)]
S28 = 14 [210 + 189]
S28 = 14 (399)
S28 = 5586