Answer
$871$
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:
$$\sum_{k=1}^{26}(3k-7) = \sum_{k=1}^{26}(3k) - \sum_{k=1}^{26}7$$
Use rule (4) above to obtain:
$$\sum_{k=1}^{26}(3k) - \sum_{k=1}^{26}7=3\sum_{k=1}^{26}k - \sum_{k=1}^{26}7$$
Use rule (1) and rule (2), respectively, to obtain:
$$3\sum_{k=1}^{26}k - \sum_{k=1}^{26}7
\\=3\left(\dfrac{26(27)}{2}\right) - 26(7)
\\=3(351) - 182
\\=1053 -182
\\=871$$
