Suatu barisan aritmetika diketahui U3=13 dan U7=33 maka suku kelimapuluh adalah

=== DERET ARITMATIKA ===

U3 = 13
U7 = 33

DItanya : U50

Jawaban :

U3 - U7 = 13 - 33
2b - 6b = - 20
- 4b = -20
b = -20/-4
b = 5

Tentukan nilai a :

U3 = a + (n-1)b
13 = a + (3-1)(5)
13 = a + 2(5)
13 = a + 10
13 - 10 = a
3 = a

=== nilai a = 3
=== nilai b = 5


Sehingga, suku ke 50 adalah:

U50 = a + (n-1)b
U50 = 3 + (50-1)(5)
U50 = 3 + 49(5)
U50 = 3 + 245
U50 = 248

U₃ = a + (3 - 1)b
13 = a + 2b

U₇ = a + (7 - 1)b
33 = a + 6b

Eliminasi
a + 2b = 13
a + 6b = 33
_________ -
-4b = -20
b = -20/-4
b = 5

Substitusi
a + 2b = 13
a + 2(5) = 13
a + 10 = 13
a = 13 - 10
a = 3

Maka
U₅₀ = a + (n - 1)b
U₅₀ = 3 + (50 - 1)5
U₅₀ = 3 + (49)(5)
U₅₀ = 3 + 245
U₅₀ = 248