Question

tuliskan 5 Suku pertama barisan berikut
a. Un = 3n-1
b. Un =1/2n² - 2
c Un=2n/5
d. Un = n+n ² - 2​

Answer 1

a. 2, 5, 8, 11, 14

b. -³⁄₂ 0, ⁵⁄₂, 6, ²¹⁄₂

c. ²⁄₅, ⁴⁄₅, ⁶⁄₅, ⁸⁄₅, ¹⁰⁄₅

d. 0, 4, 10, 18, 28

Penjelasan dengan langkah-langkah :

a. Uₙ = 3n - 1

U₁ = 3(1) - 1 = 3 - 1 = 2

U₂ = 3(2) - 1 = 6 - 1 = 5

U₃ = 3(3) - 1 = 9 - 1 = 8

U₄ = 3(4) - 1 = 12 - 1 = 11

U₅ = 3(5) - 1 = 15 - 1 = 14

∴ 5 suku pertama adalah 2, 5, 8, 11, 14

b. Uₙ = ¹⁄₂n² - 2

U₁ = ¹⁄₂(1)² - 2 = 1⁄2 - 2 = -³⁄₂

U₂ = ¹⁄₂(2)² - 2 = 2 - 2 = 0

U₃ = ¹⁄₂(3)² - 2 = ⁹⁄₂ - 2 = ⁵⁄₂

U₄ = ¹⁄₂(4)² - 2 = 8 - 2 = 6

U₅ = ¹⁄₂(5)² - 2 = ²⁵⁄₂ - 2 = ²¹⁄₂

∴ 5 suku pertama adalah -³⁄₂ 0, ⁵⁄₂, 6, ²¹⁄₂

c. Uₙ = ²ⁿ⁄₅

U₁ = ²⁽¹⁾⁄₅ = ²⁄₅

U₂ = ²⁽²⁾⁄₅ = ⁴⁄₅

U₃ = ²⁽³⁾⁄₅ = ⁶⁄₅

U₄ = ²⁽⁴⁾⁄5 = ⁸⁄₅

U₅ = ²⁽⁵⁾⁄₅ = ¹⁰⁄₅

∴ 5 suku pertama adalah ²⁄₅, ⁴⁄₅, ⁶⁄₅, ⁸⁄₅, ¹⁰⁄₅

d. Uₙ = n + n² - 2

U₁ = 1 + 1² - 2 = 2 - 2 = 0

U₂ = 2 + 2² - 2 = 6 - 2 = 4

U₃ = 3 + 3² - 2 = 12 - 2 = 10

U₄ = 4 + 4² - 2 = 20 - 2 = 18

U₅ = 5 + 5² - 2 = 30 - 2 = 28

∴ 5 suku pertama adalah 0, 4, 10, 18, 28