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