Tentukan jumlah dari deret geometri 27+9+3+1+….+1/81

Jawab:

Penjelasan dengan langkah-langkah:

a = 27

r = U2/U1

r = 9/27

r = 1/3

Un = 1/81

a . rⁿ⁻¹ = 1/81

27 . (1/3)ⁿ⁻¹ = 3⁻⁴

3³ . (3⁻¹)ⁿ⁻¹ = 3⁻⁴

3³⁻ⁿ⁺¹ = 3⁻⁴

4 – n = -4

4 + 4 = n

n = 8

Sn = a . (1 – rⁿ)/(1 – r)

S8 = 27 . (1 – (1/3)⁸)/(3/3 – 1/3)

S8 = 27 . (6.561/6.561 – 1/6.561) / (2/3)

S8 = 27 . 6.560/6.561 . 3/2

S8 = 3.280/81

S8 = 40  40/81

Detail jawaban

Kelas 9

Mapel 2 – Matematika

Bab 2 – Barisan dan Deret Bilangan

Kode Kategorisasi : 9.2.2

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