Question

Tentukanlah nilai t agar barisan berikut menjadi barisan geometri :
a. t , t , + 2 , t + , 6
b. t -2 , t + 1 , 3t + 3

Answer 1

B.  
u1....a = t - 2
u2....ar= t + 1
u3... ar²= 3t + 3

geometri pasti :
u2/ u1 = u3 / u2
(t + 1 )   / ( t - 2)  =  3t + 3 / ( t + 1)... kali silang

(t + 1) ( t + 1) = ( 3t + 3) ( t - 2)
t² + t + t + 1 = 3t² - 6t + 3t - 6
t² + 2t + 1 = 3t² - 3t - 6
0 = 3t² - t² - 3t - 2t - 6 - 1
       2t² - 5t - 7 = 0
( 2t - 7 ) ( t  +  1)
Jadi t = 7/2  atau t = -1
urutan barisan geometrinya :
t= 7/2.....  3/2 ,  9/2,   27/2 ( r = 3,  a = 3/2)
t=-1........ -3,  0 , 0  ( r = 0,   a = -3)