Answer
$1110$
Work Step by Step
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:
$$5\sum_{k=1}^{20}k + \sum_{k=1}^{20}3
\\=5\left(\dfrac{20(21)}{2}\right) + 20(3)
\\=5(210) + 60
\\=1050 + 60
\\=1110$$
