Answer:
−186450
Explanation:
Evaluate the Summation sum from k=1 to 275 of -5k+12
The question is what is the outcome of the repeated addition k=1 + k=2 + ... + k=274 + k=275, in
(-5k + 12)
(-5k + 12) is added repeatedly for different values of k, starting with k = 1 upto and including k = 275.
The result of k = 1 is the number -5*1 +12 = 7
The result of k = 2 is the number -5*2 +12 = 2
..
The result of k = 274 is the number -5*274 +12 = -1358
The result of k = 275 is the number -5*275 +12 = -1363
That seems to be a lot of work...
To evaluate the Summation sum from k=1 to 275 of -5k+12, you can split the summation into two smaller summations Part 1) and Part 2).
First you need to understand that y = -5x + 12 is a linear equation, that results in a straight line. However the summation is not a line, but it represents only the 275 points on that line, which is given as: -5x + 12.
Part 1) Evaluate the summation sum from k=1 to 275 for -5*k.
The formula for the summation of a polynomial with degree 1 is:
-5 { n*(n+1) / 2 }
Substitute the value n=275 into the formula and make sure to multiply by the front term.
−5 * { ( 275*(275+1) / 2) }
−5 * { ( 275*(276) / 2) }
−5 * { 75900 / 2 }
−5 * 37950
−189750
Part 2) Evaluate the summation sum from k=1 to 275 for 12.
The formula for the summation of a constant (12) is n * that constant. Here n = 275
12 * 275 = 3300
Add the results of Part 1) and Part 2)
−189750 + 3300
Finally you have the answer:
−186450