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# first, second and third terms, respectively, of a geometric sequence

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The terms 140, a, 560 are the first, second and third terms, respectively, of a geometric sequence. If  a is positive, what is the value of a ?

Oct 23, 2020

#1
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The terms 140, a, 560 are the first, second and third terms, respectively, of a geometric sequence. If a is positive, what is the value of a ?

Hello Guest!

$$a=140\cdot q\\ \color{blue}140\cdot q^2=560\\ q=\sqrt{\frac{560}{140}}\\ q=2\\ a=140\cdot 2$$

$$a=280$$

The geometric sequence is 140, 280, 560.

!

Oct 23, 2020
#2
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The terms 140, a, 560 are the first, second and third terms, respectively, of a geometric sequence. If a is positive, what is the value of a ?

560 is 4 times 140, so I'd expect "a" to be 2 times 140, therefore 280

Oct 23, 2020