Question

Diketahui barisan aritmatika, U3 = 8 dan U8 = 20. Jumlah 40 suku pertama itu adalah ?
Beserta cara ya...

Answer 1

U3 = a + (n-1)b
8 = a + (3-1)b
8 = a + 2b
U8 = a + 7b = 20 => caranya samadengan U3
sistem eliminasi, a yang di eliminasi
8 = a + 2b
20 = a + 7b
=> -12 = -5b
=> b = 12/5

-> a + 2b = 8
-> a + 2.12/5 = 8
-> a + 24/5 = 8
-> a = 8 - 24/5
-> a = 16/5

Sn = n/2 (2a + (n-1)b)
S40 = 40/2 (2.(16/5) + (40-1)12/5)
       = 20 (32/5 + 468/5)
       = 20 (500/5)
       = 20 (100)
S40 = 2000