College

Find the sum of the first ten terms of the geometric progression: [tex]1, 1.3, 1.69, \ldots[/tex].

Answer :

To find the sum of the terms in the sequence given, let's first identify the terms. The sequence you've provided is: 1, 1, 3, 1.69.

Since this sequence doesn't form a clear geometric progression (G.P.), we'll assume it's a specific set of terms you want to sum up, rather than a standard G.P.

Here's how to find the sum of these terms:

1. List the terms you want to sum:
- The terms are: 1, 1, 3, 1.69

2. Add the terms together:
- Start by adding the first two terms:
[tex]\[
1 + 1 = 2
\][/tex]

- Add the result to the next term:
[tex]\[
2 + 3 = 5
\][/tex]

- Finally, add this result to the last term in the sequence:
[tex]\[
5 + 1.69 = 6.69
\][/tex]

3. Therefore, the sum of the terms is approximately 6.69.

If your objective was indeed a standard geometric progression, confirming the progression pattern and common ratio would be necessary. However, as provided, the terms sum as described above.