3.1 A quadratic number pattern $$ T_{n}=a n^{2}+b n+c $$ has a third term equal to -1 , while the first differences of the quadratic sequence are given by: $$ -12 ;-8 ;-4 $$ 3.1.1 Write down the values of the first four terms of the quadratic sequence.

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To determine the first four terms of the quadratic sequence $$ T_n = a n^2 + b n + c $$, let's analyze the given information:

1. **Third Term ($$ T_3 $$):**
   $$
   T_3 = a(3)^2 + b(3) + c = 9a + 3b + c = -1
   $$

2. **First Differences:**
   The first differences given are $$-12$$, $$-8$$, and $$-4$$. These represent:
   $$
   T_2 - T_1 = -12 \quad (1)
   $$
   $$
   T_3 - T_2 = -8 \quad (2)
   $$
   $$
   T_4 - T_3 = -4 \quad (3)
   $$

Using these equations, we can find the terms step-by-step:

- **From Equation (3):**
  $$
  T_4 = T_3 + (-4) = -1 - 4 = -5
  $$

- **From Equation (2):**
  $$
  T_2 = T_3 - (-8) = -1 + 8 = 7
  $$

- **From Equation (1):**
  $$
  T_1 = T_2 - (-12) = 7 + 12 = 19
  $$

**Thus, the first four terms of the sequence are:**

$$
T_1 = 19,\quad T_2 = 7,\quad T_3 = -1,\quad T_4 = -5
$$

**Answer:**  
The first four terms of the sequence are 19, 7, –1, and –5.
The first four terms of the sequence are 19, 7, –1, and –5.

3.1 A quadratic number pattern \( T_{n}=a n^{2}+b n+c \) has a third term equal to -1 , while the first differences of the quadratic sequence are given by: \( -12 ;-8 ;-4 \) 3.1.1 Write down the values of the first four terms of the quadratic sequence.

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