Kunci Jawaban Latihan 2.5 Halaman 57 Nomor 1-3 Matematika Kelas X SMA Kurikulum Merdeka

b. 1/27 + 1/9 + … + 243

Jawaban:

a. 1 + 5/3 + 7/3 + … + 23/3

a = 1

b = 7/3 – 5/3 = 2/3

U_n = 23/3

a + (n – 1) b = 23/3

1 + (n – 1) 2/3 = 23/3

1 + 2/3 n – 2/3 = 23/3

2/3 n = 23/3 – 1/3

n = 22/3 / 2/3 = 22/3 ∙ 3/2 = 11

Baca Juga: Pengertian dan Rumus Deret Aritmetika, Bab 2 Matematika Kelas X SMA Kurikulum Merdeka

S₁₁ = 11/2 (a + U₁₁) = 11/2 (1 + 23/3) = 11/2 ∙ 26/3 = 143/3

b. 1/27 + 1/9 + … + 243

a = 1/27

r = 1/9 / 1/27 = 3

U_n = 243

a ∙ rⁿ = 243

1/27 ∙ 3ⁿ = 243

3ⁿ = 243 : 1/27 = 243 ∙ 27 = 3⁵ ∙ 3³ = 3⁸

n = 8

S_n = a (rⁿ – 1) / r – 1 = 1/27 (6.560) / 2 = 3.280 / 27

Nah, itulah dia jawaban Latihan 2.5 halaman 57 nomor 1-3 buku Matematika kelas X SMA Kurikulum Merdeka.

Baca Juga: Menentukan Barisan Geometri, Latihan 2.2 Halaman 45 Matematika Kelas X SMA Kurikulum Merdeka

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