The fifth term of an arithmetic sequence is 11 and the tenth term is 41. what is the first term?

In this sequence, the first term is and every successive term is determined by

where is the common difference between terms. We have

so that

Then

The first term is -13.

Step-by-step explanation:

The general rule of an arithmetic sequence is the following:

In which d is the common diference between each term.

This is the case going from one term to the next. However, when, as in this problem, we have the fifth and the tenth term, this formula can be expanded, as the following way:

So

The common diference is 6.

To find the first term, we do:

The first term is -13.

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).