Answer
$871$
Work Step by Step
Recall the formulas:
$A) \displaystyle \sum_{k=1}^{n} k =\dfrac{n(n+1)}{2}$
$B) \sum_{k=1}^{n} c=c+c+c+...+c=cn $
$C) \sum_{k=1}^{n} (k-c) = \sum_{k=1}^{n} k- \sum_{k=1}^{n} c $
$D) \sum_{k=1}^{n} (c k)=c \sum_{k=1}^{n} (k) $
Use formula $(C)$ to obtain:
$\displaystyle \sum_{k=1}^{26} (3k-7) = \sum_{k=1}^{26} (3k) - \sum_{k=1}^{26} (7)$
Use formula $(D)$ to obtain:
$\displaystyle \sum_{k=1}^{26} (3k) -\sum_{k=1}^{26} (7)=3 \sum_{k=1}^{26} (k)-\sum_{k=1}^{26} (7)$
Finally, apply formulas $(A)$ and $(B)$ to obtain:
$3 \displaystyle \sum_{k=1}^{26} (k)-\sum_{k=1}^{26} (7) = (3) [\dfrac{26(26+1)}{2}]-(26)(7) \\=1053-182 \\=871$
