Question

find the sum by adding each term together. use the summation capabilities of a graphing utility to verify your result.
\\(\sum_{i = 1}^{6} (2i + 7)\\)

Explanation:

Step1: Expand the summation

Substitute $i=1,2,3,4,5,6$ into $2i+7$:
$(2(1)+7)+(2(2)+7)+(2(3)+7)+(2(4)+7)+(2(5)+7)+(2(6)+7)$

Step2: Calculate each term

$9 + 11 + 13 + 15 + 17 + 19$

Step3: Sum the terms

Add the values sequentially:
$9+11=20$; $20+13=33$; $33+15=48$; $48+17=65$; $65+19=84$

Answer:

84