The first two terms of a geometric sequence are 4 and 5.8. Find the third term. Round answer to four places after the decimal point.

Third term = 

To find the third term of a geometric sequence, we need to follow these steps:

1. The first term \( a_1 = 4 \).
2. The second term \( a_2 = 5.8 \).
3. A geometric sequence follows the relationship:
   \[
   a_n = a_1 \cdot r^{n-1}
   \]
   where \( r \) is the common ratio between consecutive terms.

4. To find \( r \), we can use the ratio of the second term to the first term:
   \[
   r = \frac{a_2}{a_1} = \frac{5.8}{4} = 1.45
   \]

5. Now, we can find the third term \( a_3 \) using the formula:
   \[
   a_3 = a_1 \cdot r^2
   \]
   Substituting the values:
   \[
   a_3 = 4 \cdot (1.45)^2
   \]

Let's calculate the third term.The third term of the geometric sequence is \( 8.4100 \), rounded to four decimal places.

Would you like further details or explanations? Here are five related questions for practice:

1. What is the fourth term of the sequence?
2. How would you find the 10th term of this geometric sequence?
3. If the first term was 3 instead of 4, what would the common ratio be?
4. How do you derive the formula for the nth term in a geometric sequence?
5. What is the sum of the first three terms of this geometric sequence?

**Tip**: In geometric sequences, the common ratio can be found by dividing any term by the previous one!

The first two terms of a geometric sequence are 4 and 5.8. Find the third term. Round answer to four places after the decimal point.

Discover how to calculate the third term of a geometric sequence where the first two terms are 4 and 5.8. This solution explains the formula for geometric sequences, including the common ratio calculation and exponentiation. The final answer is rounded to four decimal places. Suitable for students in Grades 8-10.

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