4,6,9,...

Sum of a finite geometric series:

Sum of a finite geometric series:

S, start subscript, n, end subscript, equals, start fraction, a, start subscript, 1, end subscript, minus, a, start subscript, 1, end subscript, r, to the power n , divided by, 1, minus, r, end fraction

*Sn*​=1−*ra*1​−*a*1​*rn*​

It seems you are asking for the sum of a finite geometric series, but the sequence you provided—4, 6, 9, …—does not follow a geometric progression because the ratio between consecutive terms is not constant. Let's first determine the type of sequence you have.

The given sequence is:
\[
4, 6, 9, \dots
\]

**Step 1: Check for a common difference (arithmetic sequence)**

To see if this sequence is arithmetic, let's check the difference between consecutive terms:
\[
6 - 4 = 2
\]
\[
9 - 6 = 3
\]
Since the difference is not constant, this is not an arithmetic sequence.

**Step 2: Check for a common ratio (geometric sequence)**

To check for a geometric sequence, we need to divide consecutive terms:
\[
\frac{6}{4} = 1.5
\]
\[
\frac{9}{6} = 1.5
\]
The ratio is not constant either, so it’s neither arithmetic nor geometric.

If you're trying to solve a geometric series, can you confirm the correct sequence or clarify if you want to apply the formula for a different problem?

For reference, the formula for the sum of a finite geometric series is:
\[
S_n = \frac{a_1 (1 - r^n)}{1 - r}
\]
where:
- \( S_n \) is the sum of the first \( n \) terms,
- \( a_1 \) is the first term,
- \( r \) is the common ratio,
- \( n \) is the number of terms.

Feel free to provide more details, and I'll help you further! 

Here are 5 related questions:
1. How do you find the sum of an arithmetic series?
2. What is the difference between an arithmetic and geometric series?
3. How can you find the sum of an infinite geometric series?
4. How do you derive the formula for the sum of a finite geometric series?
5. What happens when the common ratio \( r \) is greater than 1 in a geometric series?

**Tip:** Always check if the ratio or difference between terms is consistent to determine if a sequence is arithmetic or geometric.

Learn how to identify if a sequence is arithmetic or geometric with a detailed analysis of the sequence 4, 6, 9,... This explanation covers how to check for common differences and ratios. Suitable for students in Grades 8-10.

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