find the sum of the first 6 term of a geometric sequence whose first term is 2 and common rotio 2/3

To find the sum of the first 6 terms of a geometric sequence, you can use the formula for the sum of the first \( n \) terms:

\[
S_n = \frac{a(1 - r^n)}{1 - r}
\]

Where:
- \( S_n \) is the sum of the first \( n \) terms.
- \( a \) is the first term.
- \( r \) is the common ratio.
- \( n \) is the number of terms.

Given:
- \( a = 2 \)
- \( r = \frac{2}{3} \)
- \( n = 6 \)

Now, substitute these values into the formula:

\[
S_6 = \frac{2(1 - \left(\frac{2}{3}\right)^6)}{1 - \frac{2

Learn how to find the sum of the first 6 terms of a geometric sequence with a detailed step-by-step solution. This problem involves a geometric sequence with the first term 2 and a common ratio of 2/3. Suitable for students in Grades 10-12.

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