Question

Find the sum of the series and show your process for finding each term leading to the final sum.

Answer 1

ANSWER

$\sum_{k=3}^5( - 2k + 5) = - 9$

EXPLANATION

The given series is

$\sum_{k=3}^5( - 2k + 5)$

This series is finite.

The expanded form is

$\sum_{k=3}^5( - 2k + 5) = ( - 2 \times 3 + 5) + ( - 2 \times 4 + 5) + ( - 2 \times 5 + 5)$

This simplifies to

$\sum_{k=3}^5( - 2k + 5) = ( - 6 + 5) + ( - 8+ 5) + ( - 10+ 5)$

$\sum_{k=3}^5( - 2k + 5) = ( - 1) + ( - 3) + ( - 5)$

$\sum_{k=3}^5( - 2k + 5) = - 9$