Penjelasan dengan langkah-langkah:

Un = an² + bn + c

U₁ = 1

a(1)² + b(1) + c = 1

a + b + c = 1 .................. (1)

U₂ = 7

a(2)² + b(2) + c = 7

4a + 2b + c = 7 ........... (2)

U₃ = 16

a(3)² + b(3) + c = 16

9a + 3b + c = 16 ....... (3)

eliminasi (2) dan (1)

4a + 2b + c = 7

. a + b + c = 1

---------------------- --

3a + b = 6 ................... (4)

eliminasi (3) dan (2)

9a + 3b + c = 16

4a + 2b + c = 7

----------------------- --

5a + b = 9 ................... (5)

eliminasi (5) dan (4)

5a + b = 9

3a + b = 6

-------------- --

2a = 3

a = 3/2 ........*

subtitusikan nilai ke(4)

3a + b = 6

3(3/2) + b = 6

9/2 + b = 6

b = 6 - 9/2

b = 12/2 - 9/2

b = 3/2 ...........*

subtitusikan nilai a dan b ke (1)

a + b + c = 1

3/2 + 3/2 + c = 1

3 + c = 1

c = 1 - 3

c = -2

rumus suku ke n

Un = 3/2n² + 3/2n - 2

Un = 1/2(3n² + 3n - 4)

suku ke 100 (U₁₀₀)

U₁₀₀ = 1/2[3(100)² + 3(100) - 4]

U₁₀₀ = 1/2[30.000 + 300 - 4]

U₁₀₀ = (15.000 + 150 - 2)

U₁₀₀ = 15.148

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