## College Algebra (10th Edition)

$1110$
RECALL: (1) $$\sum_{i=1}^{n}k = \dfrac{n(n+1)}{2}$$ (2) For any constant $c$, $$\sum_{i=1}^{n}c = nc$$ (3) For any constant $c$, $$\sum_{k=1}^{n}(k+c) = \sum_{k=1}^{n}k + \sum_{k=1}^{n}c$$ (4) For any constant $c$, $$\sum_{k=1}^{k}ck = c\sum_{k=1}^{n}k$$ Use rule (3) above to obtain: $$\sum_{k=1}^{20}(5k+3) = \sum_{k=1}^{20}(5k) + \sum_{k=1}^{20}3$$ Use rule (4) above to obtain: $$\sum_{k=1}^{20}(5k) + \sum_{k=1}^{20}3=5\sum_{k=1}^{20}k + \sum_{k=1}^{20}3$$ Use rule (1) and rule (2), respectively, to obtain: $$5\sum_{k=1}^{20}k + \sum_{k=1}^{20}3 \\=5\left(\dfrac{20(21)}{2}\right) + 20(3) \\=5(210) + 60 \\=1050 + 60 \\=1110$$