SOLUTION: The 3rd and 6th terms of a gp are 108 and _32 respectively find the common ratio and the first term

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Question 1007120: The 3rd and 6th terms of a gp are 108 and _32 respectively find the common ratio and the first term
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!

The gp is:

______, _____, 108, ____, _____,    32, _____, _____, ...


which is actually this sequence:

108/r², 108/r, 108, 108r, 108r², 108r³, 108d4, 108d5, ...

So the 6th term, 32, must equal 108r³

                    32 = 108r³
                32/108 = r³
                  8/27 = r³
                 2³/3³ = r³
                (2/3)³ = r³
                   2/3 = r

The first term is 108/r² = 108/(2/3)² = 108/(4/9) = 108(9/4) = 243

Checking the sequence, we use first term 243 and common ratio 2/3

243, 162, 108, 72, 48, 32, ...

The third term is 108 and the 6th term is 32.

Edwin
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