Question

kak tolong bantu jawab tugasku kakl plis ​

Answer 1

Materi : Barisan dan Geometri

Soal Nomor 6

Pola barisan geometri

√3, 3, 3√3, ...

Suku Pertama = √3 , Rasio = √3

Maka rumus pola : Un = (√3)ⁿ

U10 = (√3)¹⁰ = 3¹⁰/² = 3⁵ = 243

Soal Nomor 7

U1 = 64 [ x = 1 , Ux = 64 ]

U4 = 1 [ y = 4 , Uy = 1 ]

Rasio

r = ( ⁴-¹ )√( 1/64 )

r = ³√(4-³)

r = 4-³/³

r = 4-¹

[ r = ¼ ]

Hasil / Result :

Pola barisan geometri

64, 16, 4, 1, ¼, ...

Suku Pertama = 64 , Rasio = ¼

Maka rumus pola : Un = 4-ⁿ+⁴

Soal Nomor 8

Bagian A

1, 2, 4, 8, ... [ a = 1 , r = 2 ]

Maka U6 = 2⁶-¹ = 2⁵ = 32

Bagian B

3, 6, 12, 24, ... [ a = 3 , r = 2 ]

Maka U6 = 3(2⁶-¹) = 3(2⁵) = 3(32) = 96

Bagian C

27, 9, 3, 1, ... [ a = 27 , r = ⅓ ]

Maka U6 = 3-⁶+⁴ = 3-² = -⅑

Bagian D

2, -6, 18, -54, ... [ a = 2 , r = -3 ]

Maka U6 = 2(-3)⁶-¹ = 2(-3)⁵ = 2(-243) = -486

Soal Nomor 9

Pola barisan geometri

4, 12, 36, ...

Suku Pertama = 4 , Rasio = 12/4 = 3

Maka rumus pola : Un = 4(3ⁿ-¹)

Un = a( rⁿ-¹ ) = 4(3ⁿ-¹)

Soal Nomor 10

U1 = 5 [ x = 1 , Ux = 5 ]

U3 = 45 [ y = 3 , Uy = 45 ]

Rasio

r = ( ³-¹ )√(45/5)

r = ²√9

r = √9

[ r = 3 ]

Hasil / Result :

Pola barisan geometri

5, 15, 45, 135, ...

Suku Pertama = 5 , Rasio = 3

Maka rumus pola : Un = 5(3ⁿ-¹)

Jika Un = 1.215

5(3ⁿ-¹) = 1.215

3ⁿ-¹ = 1.215

3ⁿ-¹ = 243

3ⁿ-¹ = 3⁵

3ⁿ = 3⁵+¹

3ⁿ = 3⁶

[ n = 6 ] => 1.215 adalah suku ke - 6

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