1 . You are given the terms $$ 3 ; y ; 75 $$ which form a geometric sequence. What is the value of $$ y $$ if $$ y0 $$ ? Give all possible answers.

Question

1 . You are given the terms $$ 3 ; y ; 75 $$ which form a geometric sequence. What is the value of $$ y $$ if $$ y>0 $$ ? Give all possible answers.

UpStudy AI · Accepted Answer

1. Let the common ratio be $$ r $$. Then, in a geometric sequence, we have
   $$
   \frac{y}{3} = \frac{75}{y} = r.
   $$
   
2. Equating the two expressions gives
   $$
   \frac{y}{3} = \frac{75}{y}.
   $$
   
3. Cross-multiply to obtain
   $$
   y^2 = 3 \times 75 = 225.
   $$
   
4. Taking the square root of both sides yields
   $$
   y = \sqrt{225} = 15 \quad \text{or} \quad y = -15.
   $$
   
5. Since $$ y > 0 $$, the acceptable solution is
   $$
   y = 15.
   $$
$$ y = 15 $$

1 .
You are given the terms

which form a geometric sequence. What is the
value of if ? Give all possible answers.

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1 . You are given the terms which form a geometric sequence. What is the value of if ? Give all possible answers.