Evaluate
100
å (100 – 2K)
K=5
thank u so much
Hello, Steph07!
Evaluate: .$\displaystyle \sum^{100}_{k=5}(100-2k)$
We have: .$\displaystyle S \;=\;90 + 88 + 86 + \hdots - 96 - 98 - 100$
This is an arithmetic series with:
. . first term $\displaystyle a = 90$, common difference $\displaystyle d = -2$, and $\displaystyle n = 146$ terms.
The sum is: .$\displaystyle S \;=\;\frac{n}{2}\bigg[2a + (n-1)d\bigg] \;=\;\frac{146}{2}\bigg[2(90) + 145(-2)\bigg] \;=\;\boxed{-8030}$