Answer:
50
Step-by-step explanation:
Sum of all even numbers from 2 to 100:
The formula we will use is [tex]S_n=\frac{n}{2}(a+l)[/tex]
Where
n is the number of numbers
a is the first term
l is the last term
Here,
from 2 to 100, there are 100/2 = 50 terms (n=50)
first term, a = 2
last term, l= 100
So we have:
[tex]S_n=\frac{n}{2}(a+l)\\S_{50}=\frac{50}{2}(2+100)\\=2550[/tex]
Sum of all odd numbers from 1 to 99:
Here, we will use a different formula for S_n.
[tex]S_n=\frac{n}{2}(2a+(n-1)d)[/tex]
From 1 to 99, there are 50 odd numbers (n = 50)
a is the first term, a = 1
d is the common difference, the difference in successive terms, the sequence is basically 1, 3, 5... so d = 3 - 1 =2
Now, we substitute and find:
[tex]S_{50}=\frac{50}{2}(2(1)+(50-1)(2))\\S_{50}=2500[/tex]
So, subtracting Alice's result (2500) FROM Tom's (2550), we get:
2550 - 2500 = 50
Joe's result is 50
