Answer:
<u>There are 17 terms in the sequence</u>
Step-by-step explanation:
<u>Arithmetic Sequence
</u>
An arithmetic sequence is a list of numbers with a definite pattern by which each term is calculated by adding or subtracting a constant number called common difference to the previous term. If n is the number of the term, then:
Where an is the nth term, a1 is the first term, and r is the common difference.
In the problem at hand, we are given the first term a1=13, the last term an=-23, and the common difference r=-2 1/4. Let's solve the equation for n:
We need to express r as an improper or proper fraction:
Substituting:
n=17
There are 17 terms in the sequence
Answer:
y = 7
Step-by-step explanation:
calculate the slope m using the gradient formula
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
with (x₁, y₁ ) = (- 5, 10) and (x₂, y₂ ) = (3, y)
m = 
= 
For this to equal - 
since the denominators are equal, equate the numerators
y - 10 = - 3 ( add 10 to both sides )
y = 7
1. Let the first integer be represented by: 2k
the second integer by: 2(k+1)
the third integer by: 2(k+2)
and the fourth by: 2(k+3)
Then, 2k + 2(k+2) = 2(k+3) - 6
2k + 2k + 4 = 2k + 6 - 6
4k + 4 = 2k
4 = -2k
-2 = k
Answer: -4, -2, 0, 2
******************************************************************
2. Let the first integer be represented by: 2k+1
the second integer by: 2k+3
the third integer by: 2k+5
and the fourth by: 2k+7
Then, 2k+7 = (2k+1) + (2k+3) + (2k+5) + 2
2k + 7 = 6k + 11
-4 = 4k
-1 = k
Answer: -1, 1, 3, 5
Answer: the length of one side of the bedroom is 24 feet.
the length of one side of the closet is 3 feet
Step-by-step explanation:
Let x represent the length of one side of the bedroom.
Let y represent the length of one side of the closet.
The sides of the bedroom were 8
times as large as the sides of the closet. This means that
x = 8y
the sum of the areas of the two was
585 square feet. The area of the room is x^2 and the area of the closet is y^2. Therefore,
x^2 + y^2 = 585 - - - -- - - -1
Substituting x = 8y into equation 1, it becomes
(8y)^2 + y^2 = 585
64y^2 + y^2 = 585
65y^2 = 585
y^2 = 585/65 = 9
Take square root of both sides of the equation,
y = √9 = 3
x = 8y = 8×3 = 24
Answer:
2
Step-by-step explanation:
a_{7}=30-4*7=30-28=2
