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

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**Given:**
- The first three terms of an arithmetic progression (AP) are $$ a $$, $$ a + d $$, and $$ a + 2d $$, where $$ a $$ is the first term and $$ d $$ is the common difference.
- The sum of the first three terms is 27.
- The product of the first two terms is 36.

**Step 1: Express the Sum of the First Three Terms**
$$
a + (a + d) + (a + 2d) = 3a + 3d = 27
$$
$$
3(a + d) = 27
$$
$$
a + d = 9 \quad \text{(Equation 1)}
$$

**Step 2: Express the Product of the First Two Terms**
$$
a \times (a + d) = 36
$$
From Equation 1, substitute $$ a + d = 9 $$:
$$
a \times 9 = 36
$$
$$
a = 4
$$

**Step 3: Find the Common Difference $$ d $$**
Using Equation 1:
$$
4 + d = 9
$$
$$
d = 5
$$

**Step 4: Determine the First Three Terms**
$$
\text{First term} = a = 4
$$
$$
\text{Second term} = a + d = 4 + 5 = 9
$$
$$
\text{Third term} = a + 2d = 4 + 2(5) = 14
$$

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

**Answer:**
The first three terms of the arithmetic progression 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 progressi
is 27 . The product of the first 2 terms is 36 . What are the first 3 ter
of the progression?

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