ANSWER
[tex]\sum_{k=3}^5( - 2k + 5) = - 9[/tex]
EXPLANATION
The given series is
[tex]\sum_{k=3}^5( - 2k + 5)[/tex]
This series is finite.
The expanded form is
[tex]\sum_{k=3}^5( - 2k + 5) = ( - 2 \times 3 + 5) + ( - 2 \times 4 + 5) + ( - 2 \times 5 + 5)[/tex]
This simplifies to
[tex]\sum_{k=3}^5( - 2k + 5) = ( - 6 + 5) + ( - 8+ 5) + ( - 10+ 5)[/tex]
[tex]\sum_{k=3}^5( - 2k + 5) = ( - 1) + ( - 3) + ( - 5)[/tex]
[tex]\sum_{k=3}^5( - 2k + 5) = - 9[/tex]
