Find the 15th term in the following arithmetic sequence
1, 6, 11, 16, ...

15th term is 71

Step-by-step explanation:

Explicit Rule for arithmetic sequence is: Tn = a + (n - 1)*(d), where a is the first term and d is the common difference

The first term is 1, hence a = 1

The common difference is 5 (6 - 1 = 5, 11 - 6 = 5...), hence d = 5

Tn = 1 + (n - 1)*(5)

We are trying to find the 15th number.

T₁₅ = 1 + (15 - 1)*(5)

     = 1 + (14)*(5)

     = 1 + 70

     = 71

x=-2

infinite number of lines, so there is an infinite number of equations.

step-by-step explanation:

there are an infinite number of line that passes through the point (-2,5)

x=-2   is one line that passes through the point

y = 5 is another line that passes through the point

(these two lines are perpendicular to each other).

since the number of   numbers are infinite and the slope is the ratio of two numbers,(change in y over change in x) we can have an infinite number of slopes.     our only condition is that it passes through the point (-2,5)