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?

Let's denote the first term of the arithmetic progression as \( a \), and the common difference as \( d \). The first three terms can be expressed as \( a \), \( a + d \), and \( a + 2d \). According to the problem, the sum of these three terms is: \[ a + (a + d) + (a + 2d) = 3a + 3d = 27 \] This simplifies to \( a + d = 9 \) (Equation 1). Next, the product of the first two terms is given as: \[ a(a + d) = 36 \] Substituting \( a + d \) from Equation 1 gives: \[ a \cdot 9 = 36 \] This simplifies to \( a = 4 \). Now, substituting \( a \) back into Equation 1: \[ 4 + d = 9 \] \[ d = 5 \] Thus, the first three terms are: - First term: \( a = 4 \) - Second term: \( a + d = 4 + 5 = 9 \) - Third term: \( a + 2d = 4 + 2(5) = 14 \) So, the first three terms of the arithmetic progression are \( 4, 9, 14 \).