Write the first five terms of the geometric sequence with the first term, a1=4, and common ratio , r=3

To find the first five terms of the geometric sequence, we use the formula for the \(n\)th term of a geometric sequence:

\[
a_n = a_1 \cdot r^{n-1}
\]

Given:
- \(a_1 = 4\)
- \(r = 3\)

Now, we can calculate the first five terms:

1. \(a_1 = 4 \cdot 3^{0} = 4\)
2. \(a_2 = 4 \cdot 3^{1} = 12\)
3. \(a_3 = 4 \cdot 3^{2} = 36\)
4. \(a_4 = 4 \cdot 3^{3} = 108\)
5. \(a_5 = 4 \cdot 3^{4} = 324\)

So, the first five terms of the geometric sequence are **4, 12, 36, 108, 324**.

Would you like more details or have any questions?

Here are five related questions to consider:
1. What is the formula to find the \(n\)th term in a geometric sequence?
2. How do you determine the sum of the first \(n\) terms in a geometric sequence?
3. What happens to the sequence if the common ratio \(r\) is a fraction?
4. Can you find the 10th term of this sequence using the same formula?
5. How would the sequence change if the common ratio was negative?

**Tip:** In a geometric sequence, each term is found by multiplying the previous term by a constant called the common ratio.

Explore how to calculate the first five terms of a geometric sequence with the first term a1=4 and common ratio r=3. Understand the formula for the nth term of a geometric sequence and its application. Suitable for Grades 7-9 mathematics students.

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