– Penyelesaian

Diketahui :

• U2 = 2 dan U6 = 22

Ditanya :

• a, b, Un ....?

Jawaban :

Buat kedalam persamaan

Uₙ = a + (n – 1)b

U₂ = a + (2 – 1)b = 2

U₂ = a + 1b = 2 ....(1)

Uₙ = a + (n – 1)b

U₆ = a + (6 – 1)b = 22

U₆ = a + 5b = 22 ....(2)

Eliminasi, persamaan (1) dan (2)

a + 1b = 2

a + 5b = 22

___________ –

-4b = -20

b = -20/-4

b = 5

Substitusi b = 5, kedalam persamaan (1)

a + b = 2

a + 5 = 2

a = 2 – 5

a = -3

Maka, rumus suku ke-n

Uₙ = a + (n – 1)b

Uₙ = -3 + 5n – 5

Uₙ = 5n + ((-3) – 5)

Uₙ = 5n + (-8)

– Kesimpulan

Jadi,

• Suku pertama = -3
• Beda = 5
• Rumus Uₙ = 5n + (-8)