What is the sum of the first 37 terms of the arithmetic sequence? −27,−21,−15,−9,...

Enter your answer in the box.

The sum of the first 37 terms of the arithmetic sequence is 2997.

Step-by-step explanation:

Arithmetic sequence concepts:

The general rule of an arithmetic sequence is the following:

In which d is the common diference between each term.

We can expand the general equation to find the nth term from the first, by the following equation:

The sum of the first n terms of an arithmetic sequence is given by:

In this question:

We want the sum of the first 37 terms, so we have to find

Then

The sum of the first 37 terms of the arithmetic sequence is 2997.

step-by-step explanation:

the ratio of red paint to blue paint is always 9/7. that means that, whatever x's value, (4x+12)/(4x-4) has that same ratio. so, set up an equation and cross-multiply to solve for x:

9/7 = (4x+12)/(4x-4)

9(4x-4) = 7(4x+12)

36x - 36 = 28x + 84

8x - 36 = 84

8x = 120

x = 15