Question

KUIS +50:

Given that a sequence
{2, 3, 6, 11, 18, 27}
Starts from n = 0
∴ The 1st term = 3
----------------------------
a = {3, 6, 11, 18, 27}
b = .. +3+5+7+9
c = ......+2+2+2
∵ a = 3, b = 3, c = 2
aⁿ = a/(0!) + b(n-1)/(1!) + c(n-1)(n-2)/(2!)
aⁿ = a + b(n-1) + ½(c(n-1)(n-2))
aⁿ = 3 + 3(n-1) + ½(2(n-1)(n-2))
aⁿ = 3 + 3n-3 + (n-1)(n-2)
aⁿ = 3n + n² - 2n - n + 2
aⁿ = 2 + n²
Option (c)

Nah kalau rumus Uⁿ dari
{1, 3, 6, 10, 15, ....} itu apa?

Answer 1

▷ Rumus Suku Ke-n Un = 1/2n² + 1/2n

ღ Penyelesaian:

{1, 3, 6, 10, 15, ...}

Didapat :

a = U1 = 1

b = {2, 3, 4, 5, ...}

c = 1

Rumusnya :

Un = a + b ( n - 1 ) + 1/2 ( c ( n - 1 )( n - 2 ))

Un = 1 + 2 ( n - 1 ) + 1/2 ( 1 ( n - 1 )( n - 2 ))

Un = 1 + 2n - 2 + 1/2 × ( n² - 2n - n + 2 )

Un = 1 + 2n - 2 + 1/2 × ( n² - 3n + 2 )

Un = 1 + 2n - 2 + 1/2n² - 3/2n + 1

Un = 1/2n² + 2n - 3/2n

Un = 1/2n² + 1/2n

Answer 2

Jawaban:

Barisan Aritmatika Bertingkat

Rumus nya:

Pembahasan

Barisan 1, 3, 6, 10, 15, ...

1 3 6 10 15

a → 1 ~~~~~ b → 2 ~~~~~ c → 1

Substitusi deh.

atau juga bisa

Jadi, rumus Un dari barisan 1, 3, 6,10, 15,.. tersebut adalah .