Please explain clearly!
Part (a): Find the sum a + (a + 1) + (a + 2) + ... + (a + n - 1) in terms of a and n. Part (b): Find all pairs of positive integers (a,n) such that n>= 2 and
a + (a + 1) + (a + 2) + ... + (a + n - 1) = 100
Part (a): Find the sum a + (a + 1) + (a + 2) + ... + (a + n - 1)in terms of a and n.
We can write the above sum as
n*a + ( 1 + 2 + 3 + ....+ n - 1 ) =
n*a + (n - 1) (n)/2 =
n [ a + ( n - 1) / 2 ] =
n [ 2a + n - 1] / 2 =
(n/2) [ 2a + n - 1 ]
b)
a=9 and n=8
a =18 and n=5
+16 
