Answer:
n = 20
Step-by-step explanation:
Sum of an arithmetic series
[tex]S_n=\dfrac{n}{2}(a+l)[/tex]
where:
- a = first term
- l = last term
- n = number of terms
Given:
- [tex]S_n=640[/tex]
- [tex]a=25[/tex]
- [tex]l=39[/tex]
Substituting the given values into the formula and solving for n:
[tex]\implies 640=\dfrac{n}{2}(25+39)[/tex]
[tex]\implies 640 \cdot 2=n(25+39)[/tex]
[tex]\implies 1280=n(25+39)[/tex]
[tex]\implies 1280=64n[/tex]
[tex]\implies n=\dfrac{1280}{64}[/tex]
[tex]\implies n=20[/tex]
