F(n) = 1st term - common difference (n - 1)
The operation is subtraction because the sequence is decreasing.
n = number of the term you are looking for
1st term = 1st number in the sequence, in this case, 16
common difference = difference between one number to the next
f(n) = 16 - 1(n-1)
Assuming we are looking for the 5th term.
f(5) = 16 - 1(5-1)
= 16 - 1(4)
= 16 - 4
= 12 * as you can see, 12 is the 5th term of the sequence.
If you are looking for the equivalent of the nth term, simply substitute n by the number you are looking for and solve the equation.
Answer:
x = 12
Step-by-step explanation:
To get the value of x, we use the mid-segment theorem of trapezoid
The theorem is that the mid-segment is half the sum of the other two segments
We have this as
;
5x - 20 = 1/2(2x + 6 + 4x + 2)
2(5x-20) = 6x + 8
5x -20 = 3x + 4
5x -3x = 4 + 20
2x = 24
x = 24/2
x = 12
Answer:
The answer is D
Step-by-step explanation:
Answer:
= (10-3) ÷ (10-1) = 7 ÷9 = 7/9
Step-by-step explanation:
As they are parallel, their slopes are the same. So if we find slope of line j we find slope of line k when we have two points of one line like (x1 , y1) and (x2 , y2) the slope of that line is (y2-y1) ÷ (x2-x1)
Answer:
x=4, y=4, λ=-16
Step-by-step explanation:
We have this 3x3 system of linear equations:
λ
λ

So, let's rewrite the system in its augmented matrix form
![\left[\begin{array}{cccc}4&0&1&0\\0&4&1&0\\1&1&0&8\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D4%260%261%260%5C%5C0%264%261%260%5C%5C1%261%260%268%5Cend%7Barray%7D%5Cright%5D)
Let´s apply row reduction process to its associated augmented matrix:
Swap R1 and R3
![\left[\begin{array}{cccc}1&1&0&8\\0&4&1&0\\4&0&1&0\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%261%260%268%5C%5C0%264%261%260%5C%5C4%260%261%260%5Cend%7Barray%7D%5Cright%5D)
R3-4R1
![\left[\begin{array}{cccc}1&1&0&8\\0&4&1&0\\0&-4&1&-32\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%261%260%268%5C%5C0%264%261%260%5C%5C0%26-4%261%26-32%5Cend%7Barray%7D%5Cright%5D)
R3+R2
![\left[\begin{array}{cccc}1&1&0&8\\0&4&1&0\\0&0&2&-32\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%261%260%268%5C%5C0%264%261%260%5C%5C0%260%262%26-32%5Cend%7Barray%7D%5Cright%5D)
Now we have a simplified system:
x+y+0=0
0+4y+λ=0
0+0+2λ=-32
Solving for λ, x, and y
λ=-16
x=4
y=4