Diketahui deret aritmetika mempunyai U₁₂ = –35, U₁₆ = –75, dan Uₙ = –415.
Jumlah deret tersebut adalah
–8.500
Pembahasan:
Rumus suku ke-n deret aritmatika
Uₙ = a + (n – 1)b
U₁₂ = –35
⇔ a + (12 – 1)b = –35
⇔ a + 11b = –35 ... (1)
U₁₆ = –75
⇔ a + (16 – 1)b = –75
⇔ a + 15b = –75 ... (2)
Eliminasi a dari persamaan (1) dan (2).
a + 11b = –35
a + 15b = –75 _
–4b = 40
b = –10
Substitusikan b = –10 ke dalam persamaan (1).
a + 11b = –35
a + 11(-10) = –35
a = –35 + 110 = 75
Diperoleh a = 75 dan b = –10
Uₙ = –415
a + (n – 1)b = –415
75 + (n – 1)–10 = –415
75 –10n + 10 = –415
–10n = –415 – 75 – 10
–10n = –500
n = –500
–10
n = 50
Jumlah n suku pertama deret aritmetika:
Sₙ = n/2(2a + (n – 1)b
Dengan demikian:
S₅₀ = 50/2(2(75) + (50 – 1)–10)
= 25(150 + 49 × (–10))
= 25(150 – 490)
= 25 × –340
= –8.500