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The third and fourth terms of a geometric sequence are 12 and 16, respectively. What is the first term of the sequence?

mathtoo  Aug 28, 2018
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The common ratio, r, can be found  by   [ successive term  /  preceding term ]  = 16 / 12 =  4/3

 

Since...to get the third term...we had to multiply the first term  by  "r"  twice...se have this equation ;

 

(first term)  * r^2  = 12

 

(first term) (4/3)^2  = 12

 

(first term) ( 16/9)   = 12     multiply both sides by   9/16

 

first term   =  12 (9/16)   = (12/16) (9) = (3/4)(9) =  27/4

 

 

cool cool cool

CPhill  Aug 28, 2018

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