Evaluate the Summation sum from n=3 to 8 of 15-4n

Problem

(∑_n=3^8)(15−4*n)

Solution

1. Identify the terms of the arithmetic series by substituting the values of n from the lower limit n=3 to the upper limit n=8

2. Calculate the first term (a_1) by substituting n=3 into the expression.

(a_1)=15−4*(3)=3

3. Calculate the last term (a_k) by substituting n=8 into the expression.

(a_k)=15−4*(8)=−17

4. Determine the number of terms k in the summation using the formula k=upper limit−lower limit+1

k=8−3+1=6

5. Apply the formula for the sum of an arithmetic series, which is (S_k)=(k*((a_1)+(a_k)))/2

(S_6)=(6*(3+(−17)))/2

6. Simplify the expression to find the final sum.

(S_6)=3*(−14)=−42

Final Answer

(∑_n=3^8)(15−4*n)=−42

Want more problems? Check here!