Find the sum of the first 10 terms of the following geometric sequences:

1526.0
1532.0
1534.5
1528.5

Question

Find the sum of the first 10 terms of the following geometric sequences: $$ \{1.5,3,6,12,24 \ldots\} $$ 1526.0 1532.0 1534.5 1528.5

UpStudy AI · Accepted Answer

To find the sum of the first 10 terms of the geometric sequence $$ \{1.5, 3, 6, 12, 24, \ldots\} $$, follow these steps:

1. **Identify the first term and the common ratio:**
   - First term ($$ a $$) = 1.5
   - Common ratio ($$ r $$) = $$ \frac{3}{1.5} = 2 $$

2. **Use the formula for the sum of the first $$ n $$ terms of a geometric sequence:**
   $$
   S_n = a \frac{r^n - 1}{r - 1}
   $$
   Plugging in the values:
   $$
   S_{10} = 1.5 \frac{2^{10} - 1}{2 - 1} = 1.5 (1024 - 1) = 1.5 \times 1023 = 1534.5
   $$

**Answer:** 1534.5
The sum of the first 10 terms is 1534.5.

Find the sum of the first 10 terms of the following geometric sequences:

1526.0
1532.0
1534.5
1528.5

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Find the sum of the first 10 terms of the following geometric sequences: 1526.0 1532.0 1534.5 1528.5

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Find the sum of the first 10 terms of the following geometric sequences:

1526.0
1532.0
1534.5
1528.5