Answer:
The rule or the sequence is : an = -3n - 1
Explanation:
* Lets look to the terms of the sequence
-4 , -7 , -10 , -13
- The difference between each two consecutive terms is:
-7 - -4 = -3 , -10 - -7 = -3 . -13 - -10 = -3
∴ It is an arithmetic sequence
* because we add a constant value to each term to find the second term
- That means a1 = a , a2 = a + d , a3 = a + 2d , ............
* The rule of any term of the arithmetic sequence is;
- an = a + (n - 1) d , where a is the first term , d is the constant
difference and n is the position of the number in the sequence
∵ a = -4 and d = -3
∴ The rule of any term in this sequence is:
* an = -4 + (n - 1)(-3)
* Lets simplify the formula
∴ an = -4 + -3n + 3
∴ an = -3n - 1
* The rule or the sequence is : an = -3n - 1