Rumus suku ke n pada barisan aritmatika

Un = a + (n – 1)b

Rumus jumlah n suku pertama

Sn = \frac{n}{2}

2

n

(2a + (n – 1)b)

Sn = \frac{n}{2}

2

n

(a + Un)

Keterangan

a = suku pertama

b = beda ⇒ b = U₂ – U₁ = U₃ – U₂ = ....

Pembahasan

Diketahui

Barisan aritmatika: \frac{1}{2},\frac{5}{6} , \frac{7}{6} , ..., \frac{21}{2}

2

1

,

6

5

,

6

7

,...,

2

21

Un = \frac{21}{2}

2

21

Ditanyakan

Nilai n

Jawab

b = U₂ – U₁

b = \frac{5}{6} - \frac{1}{2}

6

5

−

2

1

b = \frac{5}{6} - \frac{3}{6}

6

5

−

6

3

b = \frac{2}{6}

6

2

b = \frac{1}{3}

3

1

Un = \frac{21}{2}

2

21

a + (n – 1)b = \frac{21}{2}

2

21

\frac{1}{2}

2

1

+ (n – 1) \frac{1}{3} = \frac{21}{2}

3

1

=

2

21

(n – 1) \frac{1}{3} = \frac{21}{2} - \frac{1}{2}

3

1

=

2

21

−

2

1

\frac{n - 1}{3} = \frac{20}{2}

3

n−1

=

2

20

\frac{n - 1}{3}

3

n−1

= 10

(n – 1) = 10 × 3

n – 1 = 30

n = 31