To find the sum of the first 10 terms of a geometric progression (GP), we can use the formula for the sum of the first $n$ terms of a GP:

$S_n = \frac{a_1(1 - r^n)}{1 - r}$

where:

• $S_n$ is the sum of the first $n$ terms,
• $a_1$ is the first term,
• Given values a1 = -2 r = -3 n = 10

Calculate the sum of the first 10 terms using the formula

S_n = a1 * (1 - r**n) / (1 - r) S_nThe sum of the first 10 terms of the geometric progression is 29,524.

Would you like more details or have any further questions on this topic?

Here are 5 related questions to explore further:

1. How does the sum of a geometric progression change if the common ratio is positive?
2. What happens to the sum if the common ratio is between -1 and 1?
3. Can the sum of an infinite geometric progression ever be finite? If so, under what conditions?
4. How do you derive the formula for the sum of a geometric progression?
5. How can the sum of a geometric series be calculated if the common ratio is a fraction?

Tip: In geometric progressions, the sign of the common ratio significantly affects