# geometric sequence. Determine the numbers a, b if 3 ,a ,b , 24 is a geometric sequence.

The consecutive terms of a geometric sequence have a common ratio.

We have the sequence given by 3 ,a ,b , 24

24/b = b/a = a/3

=> 24a = b^2 or a = b^2/24

substitute in b/a = a/3

=> 24b/b^2 = b^2/3*24

=> 24/b = b^2/24*3

=> b^3 = 24*24*3

=> b = 3^3*8*8

=> b = 3*4

=> b = 12

a = 144/24 = 6

The value of a = 6 and b = 12
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