**Geometric Sequence Problem**---**Question 15:**If 40, \( n \), and 10 form the first three terms of a geometric sequence, then which of the following is the value of \( n \)?1. 162. 183. 204. 24**Answer Choices:**- ( ) 1- ( ) 2- ( ) 3- ( ) 4---Explanation:In a geometric sequence, each term after the first is the product of the previous term and a constant ratio \( r \). That is, the sequence can be represented as:\[ a, ar, ar^2, ... \]Given that 40, \( n \), and 10 form the first three terms of a geometric sequence:- The first term \( a \) is 40.- The second term \( n \) is \( ar \).- The third term is 10.Since the third term is \( ar^2 \), we have:\[ ar^2 = 10 \]From the first term:\[ a = 40 \]The second term:\[ ar = n \]\[ 40r = n \]Substituting \( a = 40 \) into the equation \( ar^2 = 10 \):\[ 40r^2 = 10 \]\[ r^2 = \frac{10}{40} \]\[ r^2 = \frac{1}{4} \]\[ r = \frac{1}{2} \, \text{or} \, r = -\frac{1}{2} \]If \( r = \frac{1}{2} \):\[ n = 40 \times \frac{1}{2} = 20 \]Therefore, \( n = 20 \), which corresponds to option 3.Correct Answer: **3. 20**Remember that identifying sequences and understanding their properties are crucial skills in mathematics that apply widely, from algebra to advanced calculus.

Name: **Geometric Sequence Problem**---**Question 15:**If 40, \( n \), and
Uploaded: 2024-03-20T06:38:58.000Z
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Description: **Geometric Sequence Problem**---**Question 15:**If 40, \( n \), and 10 form the first three terms of a geometric sequence, then which of the following is the value of \( n \)?1. 162. 183. 204. 24**Answer Choices:**- ( ) 1- ( ) 2- ( ) 3- ( ) 4---Exp