**Answer:**

Option A is correct

**General rule for arithmetic sequence **with and is;

**Step-by-step explanation:**

**Arithmetic sequence** states that a sequence where the difference between each successive pair of terms is the same.

**The general rule for the arithmetic sequence** is given by;

where

**a** represents the **first term**

**d** represents the** common difference** and

**n **represents the **number of terms.**

**Given: ** and

a+(3-1)d = -12 [Using arithmetic sequence rule]

a + 2d = -12

or we can write this as;

a = -12 - 2d ......[1]

Similarly, for we have;

a+7d = -37 ......[2]

Substitute equation [1] into [2] to solve for d;

-12 - 2d +7d = -37

**Combine like terms;**

-12 + 5d = -37

**Add both sides 12 we get;**

-12 + 5d + 12 = -37 + 12

Simplify:

5d = -25

**Divide both sides by 5 we get;**

**d = -5**

Substitute the value of d in equation [1] to solve for a;

a = -2(-5) - 12

a = 10 -12 = -2

∴ **a = -2**

**therefore, the general rule for the arithmetic sequence with** and is,