Question 1185943
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The geometric mean between the first TWO terms is 32, and the third term is 4; from that we can conclude that the common ratio is less than 1.<br>
Then, given that the geometric mean between the first two terms is 32, along with the fact that the common ratio is less than 1, we can do this:<br>
Let the first term be 32/x
Let the second term be 32x<br>
Then the first three terms of the geometric sequence are<br>
32/x, 32x, 4<br>
Now use the fact that the second term is the geometric mean between the first and third:<br>
{{{(32x)^2=(32/x)(4)}}}
{{{1024x^2=128/x}}}
{{{x^3=128/1024=1/8}}}
{{{x=1/2}}}<br>
The common ratio is 1/2; the terms are
32/x = 32/(1/2) = 64
32x = 32(1/2) = 16
4<br>
ANSWER: The first term is 64<br>