Question

Suatu deret aritmatika diketahui ...S5= 35
S4=24

U15= ?

Answer 1

S5 = 5/2 × ( 2a + (5-1)b)
35 = 5/2 × (2a + (5-1)b)
14 = 2a + 4b --> 1
s4 = 4/2 × ( 2a + (4-1)b)
24 = 4/2 × ( 2a + (4-1)b)
12 = 2a + 3b --> 2

1 - 2
2 = b
sub b= 2 ke 2
12 = 2a + 6
6 = 2a , a = 3
jadi a = 3, b = 2

U15 = a + (n-1)b
= 3 + 14×2
= 3 + 28
= 31

Answer 2

Sn = n/2 (2a + (n-1)b)

S5 = 35
maka
35 = 5/2 (2a + (5-1)b)
35 = 2,5 (2a + 4b)
35 = 5a + 10b
dibagi 5 semua, => 7 = a + 2b, lalu dikali 2 ==> 14 = 2a + 4b

S4 = 24
maka
24 = n/2 (2a + (n-1)b)
24 = 4/2 (2a + (4-1)b)
24 = 2 (2a + 3b)
24 = 4a + 6b
dibagi 2 semua => 12 = 2a + 3b

eliminasikan
14 = 2a + 4b
12 = 2a + 3b  -
  2 = b

a + 2b = 7
a + 4 = 7
a = 3

maka
Un = a + (n-1)b
U15 = a + (15-1)b
U15 = a + 14b
U15 = 3 + 14(2)
U15 = 3 + 28
U15 = 31