Step-by-step explanation:
arithmetic progression
even numbers between 1001 and 10000
1002,1004,.......9998
Tn=a+(n-1)d
Tn = 9998 last term in the progression of even numbers
a = 1002 first term
d = 2 distance
9998=1002+(n-1)(2)
8996=2n-2
8998=2n
n = 4499 the number of terms
sum = n/2 (a+Tn) = 4499/2(1002+9998)
= (4499/2)(11000) = 24744500
Logic:
notice what happens when you add the first and last terms
1002+9998=11000
1004+9996=11000
.......
