Question

What is the sum of the arithmetic series 18 sigma t=1 (5t-4)

A. 783
B. 1,566
C. 819
D. 86

Answer 1

`\bf \sum\limits_(t=1)^(18)~5t-4\implies \sum\limits_(t=1)^(18)~5t~~-~~\sum\limits_(t=1)^(18)~4\implies 5\sum\limits_(t=1)^(18)~t~~-~~\sum\limits_(t=1)^(18)~4 \\\\\\ 5\left[\cfrac{18(18+1)}{2} \right]~~-~~(18\cdot 4)\implies 5(171)~~-~~72 \\\\\\ 855-72\implies 783`