Question

Find the sum of the series. Include each term that leads to the final sum and show the expression for finding that term. ∑5k=3(−2k+5)

Answer 1

`\large\boxed{\sum\limits_(k=3)^5(-2k+5)=-9}`

Explanation:

`\sum\limits_(k=3)^5(-2k+5)\to a_k=-2k+5\\\\\text{Put}\ k=3,\ k=4\ \text{and}\ k=5:\\\\a_3=-2(3)+5=-6+5=-1\\a_4=-2(4)+5=-8+5=-3\\a_5=-2(5)+5=-10+5=-5\\\\\sum\limits_(k=3)^5(-2k+5)=-1+(-3)+(-5)=-9`