Evaluate the partial sum 9+12+15...+51+54+57
1 answer:
Answer:
The partial sum is 561
Step-by-step explanation:
Given:
The arithmetic series = 9+12+15...+51+54+57
Partial sum between 9 and 57, with d=3
To Find :
The partial sum = ?
Solution
The given series is a arithmetic series with difference 3.
So the series is
9,12,15,18,21,24,27,30,33,36,29,42,45,48,52,51,54,57
Thus There are 17 terms,
Here the is a middle term is the the ninth,
The 9 term is
Now the
The partial sum is 33 x 17 = 561
You might be interested in
9514 1404 393
Answer:
see below
Step-by-step explanation:
Starting from the point-slope equation ...
y -y1 = m(x -x1)
Solving for y gives ...
y = mx +(y1 -m·x1)
So, the slope-intercept form equation is fairly easily found:
y = mx +b . . . . where m = m, and b = y1-m·x1
This is the equation we have used for 'b' in the attached spreadsheet.
__
Of course, the formula for slope is ...
m = (y2 -y1)/(x2 -x1)
This is the equation we have used for 'm' in the attached spreadsheet. For all problems, we have used the first point. (It doesn't matter which point you use if there are two of them.)
__
The second attachment is the Google Sheets spreadsheet saved in ODS format. Most spreadsheet programs should be able to open that so you can see the formulas, if you're interested. (The gray values of m are computed using the two points. The unshaded values of m are entered by hand.)
_____
I'll write a couple of equations in each group so you can see how the spreadsheet numbers relate:
y = mx +b
1. y = 2x -7
3. y = 2/3x +4
8. y = 1/3x -5
9. y = -5/2x +4
