Question

Pada deret aritmetika Sn= U1 + U2+...+ Un., semua sukunya positif. Jika U1xU4 =36 dan U2xU3 = 54, maka Sn = .......

Answer 1

A ( a +3b ) = 36

a² + 3ab = 36

(a+b) (a+2b) = 54
a²+3ab + 2b² = 54
a² +3ab       = 36
---------------------     -
2b² = 18
b²= 9
b = 3

a ( a +3b ) = 36
a (a + 9) = 36
a² + 9a = 36
( a +12 ) ( a- 3)  karna smua positif ambil 
a= 3

Sn = n/2 ( 2a +(n-1)b
    = n/2 ( 6 + 3n - 3)
   = n/2 ( 3n + 3)
  = 1/2( 3n² + 3n)

TES : barisan Arit = 3,6,9,12,....
     u1 x u4 = 3 x 12 = 36
     u2 x u3 = 6 x 9 = 54