Evaluate the Summation sum from i=3 to 8 of -5i+2

Problem

(∑_i=3^8)(−5*i+2)

Solution

1. Identify the terms of the summation by substituting each integer value of i from the lower limit i=3 to the upper limit i=8

2. Calculate the value of the expression for each index:
   For i=3 −5*(3)+2=−15+2=−13
   For i=4 −5*(4)+2=−20+2=−18
   For i=5 −5*(5)+2=−25+2=−23
   For i=6 −5*(6)+2=−30+2=−28
   For i=7 −5*(7)+2=−35+2=−33
   For i=8 −5*(8)+2=−40+2=−38

3. Sum the resulting values together:

−13+(−18)+(−23)+(−28)+(−33)+(−38)

4. Simplify the addition to find the total:

−13−18−23−28−33−38=−153

Final Answer

(∑_i=3^8)(−5*i+2)=−153

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