Answer:
617.5
Step-by-step explanation:
If you expand the series by putting in [tex]n=1,n=2,n=3...[/tex] values, you will see:
- Put 1 in [tex]n[/tex], [tex]71-2.3(1)=68.7[/tex]
- Put 2 in [tex]n[/tex], [tex]71-2.3(2)=66.4[/tex]
- Put 3 in [tex]n[/tex], [tex]71-2.3(3)=64.1[/tex]
68.7, 66.4, 64.1, ....
To find common difference (d) (difference in a term and its previous term) we take any term and subtract from it the term before it:
[tex]66.4-68.7=-2.3[/tex]
The sum of arithmetic series formula is:
[tex]S_{n}=\frac{n}{2}[2a+(n-1)d][/tex]
Where,
- [tex]S_{n}[/tex] is the sum of nth term
- a is the first term (in our case it is 68.7)
- n is the term number (in our case we want to find 50th sum, so n = 50)
- d is the common difference (in our case it is -2.3)
Substituting these values, we get:
[tex]S_{50}=\frac{50}{2}[2(68.7)+(50-1)(-2.3)]\\S_{50}=25[137.4+(49)(-2.3)]\\S_{50}=25[24.7]\\S_{50}=617.5[/tex]
Last answer choice is right.
