Find an explicit formula for the arithmetic sequence 12, 5, -2, -

an = 12 -7(n-1)

an = 19-7n

Step-by-step explanation:

The explicit formula for an arithmetic sequence is

an = a1 +d(n-1) where a1 is the first term and d is the common difference

a1 =12

We find d by taking the second term and subtracting the first term

d = 5-12

d = -7

an = 12 -7(n-1)

We can simplify this

an = 12 -7n+7

an = 19-7n

To find the area of this triangle, we may use Heron's formula:
                          A = sqrt ((s)(s - a)(s - b)(s - c))
where s is the semi - perimeter, a, b, and c are the measure of the sides. 
                                  s = (a + b + c) / 2 = (10 + 10 + 16) / 2 = 18
Substituting this to the equation for area,
                         A = sqrt ((18)(18 - 10)(18 - 10)(18 - 16)) 
                                  A = 48 units²