The sum of the finite arithmetic series is 450
The series is given as:
(–5) + 0 + 5 + 10 + ... + 65
Start by calculating the number of terms (n) in the series using the following last term formula
[tex]L = a + (n - 1)d[/tex]
Where:
L represents the last term; L = 65
a represents the first term; a = -5
d represents the common difference; d = 5
n represents the number of terms
So, we have:
[tex]65 = -5 + (n - 1)*5[/tex]
Add 5 to both sides
[tex]70 = (n - 1)*5[/tex]
Divide both sides by 5
[tex]14 = n - 1[/tex]
Add 1 to both sides
[tex]n = 15[/tex]
The sum of finite terms is then calculated as:
[tex]S_n = \frac n2 \times (a + L)[/tex]
This gives
[tex]S_n = \frac {15}2 \times (-5 + 65)[/tex]
[tex]S_n = \frac {15}2 \times 60[/tex]
[tex]S_n = 450[/tex]
Hence, the sum of the finite arithmetic series is 450
Read more about arithmetic series at:
https://brainly.com/question/6561461
