Prove that the sum of `n` number of terms of two different A.P. s can be same for only one value of `ndot`

Prove that the sum of an odd number of terms in A.P is equal to the middle term mutiplied by the number of terms

Sum of n Terms of an A.P. | Examples

The sum of n terms of an A.P. is (n^(2)+5n). Its common difference is :

If the sum of first n terms of two A.P.'s are in the ratio 3n+8 : 7n+15, then the ratio of 12th term is

The sum of n terms of an A.P. is 3n^(2)+5 . The number of term which equals 159, is

The sum of first n terms of an A.P. is 5n ^(2)+ 4n, its common difference is :

If the sum of m terms of an A.P. is same as the sum of its n terms, then the sum of its (m+n) terms is

The sum of n terms of an A.P.is 3n^(2)-n. Find the first term and common difference of A.P.

Sum OF n terms || Assuming number OF terms in A.P. and illustration

The ratio of the sum of n terms of two A.P.'s is (7n+1):(4n+27). Find the ratio of their mth terms.