1. suku ke -5 suatu barisan aritmetika adalah 29. jumlah 7 suku pertamanya adalah 245. suku ke -17 barisam tersebut adalah . . .
a. -96
b. -43
c. -35
d. 35
e. 96
a. -96
b. -43
c. -35
d. 35
e. 96
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245 = 7/2 × (2a + 6b)
245 = 7(2/2) × (a + (6/2b)
245 = 7 × (a + 3b)
7 × (a + 3b) = 245
a + 3b = 245/7
a + 3b = 35/1
a + 3b = 35
a + 4b = 29
a + 3b = 35
=========== -
(4 - 3)b = (29 - 35)
1b = -6
b = -6
=================
a + (3 × (-6) = 35
a + (-18) = 35
a - 18 = 35
a = 35 + 18
a = 53
MAKA :
U17 = 53 + (16 × (-6)
= 53 + (-96)
= 53 - 96
= -(96 - 53)
= -43 (B)
Barisan Aritmatika
Suku ke-n deret aritmatika: Uₙ = a + (n - 1)b
Jumlah Suku ke-n deret aritmatika: Sₙ = n/2 × (a + Uₙ)
keterangan:
a: suku pertama
b: beda
Suku ke-5:
Uₙ = a + (n - 1)b
U₅ = a + (5 - 1)b
29 = a + 4b .................. [1]
Suku ke-7:
U₇ = a + (7 - 1)b
U₇ = a + 6b
Jumlah 7 suku pertama:
Sₙ = n/2 × (a + Uₙ)
S₇ = 7/2 × (a + U₇)
245 = 3,5a + 3,5(U₇)
245 = 3,5a + 3,5(a + 6b)
245 = 3,5a + 3,5a + 3,5(6b)
245 = 7a + 21b
35 = a + 3b .................. [2]
Eliminasi pers [1] dan [2].
a + 4b = 29
a + 3b = 35
_________-
b = -6
Substitusi.
a + 4b = 29
a + 4(-6) = 29
a - 24 = 29
a = 29 + 24
a = 53
Suku ke-17:
U₁₇ = a + (17 - 1)b
= 53 + 16(-6)
= 53 - 96
= -43
Jadi, suku ke-17 barisan tersebut adalah -43 [b.].