Question

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

∑^5k=3(−2k+5)

Please explain also

Answer 1

`\sum_(k=3)^5( - 2k + 5) = - 9`

Step-by-step 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 * 3 + 5) + ( - 2 * 4 + 5) + ( - 2 * 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`