6 / 5+i Perform the indicated operations and express the result in standard form.
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The series 7 + 16 + 25 +34 +43 +52 + 61 is an illusration of arithmetic series
The sigma notation of the series is:
The series is given as:
7 + 16 + 25 +34 +43 +52 + 61
The above series is an arithmetic series, with the following parameters
- First term, a = 7
- Common difference, d = 9
- Number of terms, n = 7
Start by calculating the nth term using:
a(n) = a + (n - 1) * d
This gives
a(n) = 7 + (n - 1) * 9
Evaluate the product
a(n) = 7 - 9 + 9n
Evaluate the difference
a(n) = 9n - 2
So, the sigma notation is:
Read more about arithmetic series at:
Answer:
Step-by-step explanation:
We know that one of the endpoints of the line segment is (x+4, 1/2y)
The midpoint of the line segment is (3, -2).
And we want to find the other coordinates in terms of x and y.
To do so, we can use the midpoint formula:
Since we know that the midpoint is (3, -2), let's substitute that for M:
Let's solve for each coordinate individually:
X-Coordinate:
We have:
We know that one of the endpoints is (x+4, 1/2y). So, let's let (x+4, 1/2y) be our (x₁, y₁). Substitute x+4 for x₁. This yields:
Solve for our second x-coordinate x₂. Multiply both sides by 2:
Subtract 4 from both sides:
Subtract x from both sides. Therefore, the x-coordinate of our second point is:
Y-Coordinate:
We have:
Substitute 1/2y for y₁. This yields:
Solve for y₂. Multiply both sides by 2:
Subtract 1/2y from both sides. So:
Therefore, the other coordinate expressed in terms of x and y is: