What is the rule for the sequence corresponding to this series? –4 + –7 + –10 + –13

The rule or the sequence is : an = -3n - 1

Step-by-step 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