The problem asks to calculate the 15th term of a geometric progression where the first term $a$ is 8 and the common ratio $r$ is 2.

1. Problem Description

The problem asks to calculate the 15th term of a geometric progression where the first term $a$ is 8 and the common ratio $r$ is

2.

2. Solution Steps

The formula for the nth term of a geometric progression is given by:

$S_n = a \frac{r^n - 1}{r-1}$

where $a$ is the first term, $r$ is the common ratio, and $n$ is the number of terms.

In this case, we are given $a = 8$, $r = 2$, and $n = 15$. We want to find the sum of the first 15 terms.

Substituting these values into the formula, we get:

$S_{15} = 8 \frac{2^{15} - 1}{2 - 1}$

$S_{15} = 8 \frac{32768 - 1}{1}$

$S_{15} = 8 \times 32767$

$S_{15} = 262136$

There seems to be a slight calculation error in the given solution. Let's recalculate:

$S_{15} = 8 * (2^{15} - 1)/(2-1) = 8 * (32768 - 1) / 1 = 8 * 32767 = 262136$

The OCR result gives

2

6

2

1

4

4. But $8 * 32768=262144$, while the formula is $S_n = a \frac{r^n - 1}{r-1}$, so the answer is $8 * (2^{15}-1)$.

3. Final Answer

262136