- #1
subhradeep mahata
- 120
- 13
Homework Statement
In an AP, sum of first n terms is equal to m and sum of first m terms is equal to n. Then, find the sum of first (m-n) terms in terms of m and n, assuming m>n.
Homework Equations
Sum of an AP: n/2 * {2a+ (n-1)d}
The Attempt at a Solution
We get two equations:
m= n/2 * {2a+ (n-1)d} and
n= m/2 * {2a+ (m-1)d}
where a and d are first term and common difference respectively. Now, we can solve for a and d separately and plug the values in this equation:
Sm-n = (m-n)/2 * {2a + (m-n-1)d}
But, as we can see it is a very lengthy and ambiguous method. Can someone please find an easier method for the problem?