Hey guys please try this is kinda urgent. what is the value of x in the geometric progression. 16/9 , x, 1, y.

Question

asked Jul 25, 2022 193k views

1 Answer

Maxbeizer · Answer 1 · 2022-07-30T14:41:34+0000

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Step-by-step explanation:

Let r be the common ratio. Also, we'll make r nonzero, i.e.
$r \\e 0$

Multiplying this common ratio by any term gets us the next term of the geometric sequence.

16/9 is the first term, so that makes (16/9)*r the second term

Since (16/9)r is the second term, the third term is (16/9)r*r = (16/9)r^2

Set this equal to 1 and solve for r.

(16/9)r^2 = 1

r^2 = 1*(9/16)

r^2 = 9/16

r = sqrt(9/16) or r = -sqrt(9/16)

r = 3/4 or r = -3/4

Now that we know what r is, we can determine the second term

If r = 3/4, then,

(16/9)*r = (16/9)*(3/4) = 4/3

Or if r = -3/4, then,

(16/9)*r = (16/9)*(-3/4) = -4/3

So the second term is either 4/3 or -4/3 depending on which r value you go for.