15. The sum of the first 3 consecutive terms of an arithmetic progression is 27 . The product of the first 2 terms is 36 . What are the first 3 terms is of the progression?

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Let's denote the first three terms of the arithmetic progression (AP) as $$ a $$, $$ a + d $$, and $$ a + 2d $$, where $$ a $$ is the first term and $$ d $$ is the common difference.

1. **Sum of the first three terms:**
   $$
   a + (a + d) + (a + 2d) = 3a + 3d = 27
   $$
   Simplifying:
   $$
   a + d = 9 \quad \text{(Equation 1)}
   $$

2. **Product of the first two terms:**
   $$
   a \times (a + d) = 36
   $$
   Using Equation 1 ($$ a + d = 9 $$):
   $$
   a \times 9 = 36 \implies a = 4
   $$

3. **Finding the common difference $$ d $$:**
   Substitute $$ a = 4 $$ into Equation 1:
   $$
   4 + d = 9 \implies d = 5
   $$

4. **First three terms of the AP:**
   $$
   \begin{align*}
   \text{First term} &= a = 4, \
   \text{Second term} &= a + d = 4 + 5 = 9, \
   \text{Third term} &= a + 2d = 4 + 10 = 14.
   \end{align*}
   $$

**Verification:**
- Sum: $$ 4 + 9 + 14 = 27 $$
- Product: $$ 4 \times 9 = 36 $$

Thus, the first three terms of the progression are **4, 9, and 14**.

**Answer:**  
The first three terms are 4, 9, and 14.
The first three terms of the arithmetic progression are 4, 9, and 14.

The sum of the first 3 consecutive terms of an arithmetic progression
is 27 . The product of the first 2 terms is 36 . What are the first 3 terms
is of the progression?

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