In the expansion of `(x+a)^n` if the sum of odd terms is `P` and the sum of even terms is `Q ,` then

If n is a positive integer, show that, in the expansion of (1+x)^(n) the sum of the coefficents of terms in the odd positions is equal to the sum of the cofficients of term in the even positions and each sum is equal to 2^(n-1) .

An A.P. consists of n terms. If the sum of its first three terms is x and the sum of the last three terms is y, then show that, the sum of all the terms of the A.P. is (n)/(6)(x+y) .

The sum of first three terms of an arithmetic progression with n terms is x and the sum of last three terms is y.Show that the sum of n terms is n/6(x+y)

The number of terms of an A.P. is even. The sum of the odd terms is 24, and of the even terms is 30, and the last term exceeds the first by 10 1/2 then the number of terms in the series is a. 8 b. 4 c. 6 d. 10

In a GP , the ratio of the sum of the first eleven terms of the sum of the last even terms is 1//8 and the ratio of the sum of all the terms without the first nine to the sum of all terms without the last nine is 2 . Then the number of terms in the GP is

If in an arithmetic progression, the sum of n terms is equal to the sum of r terms then the sum of (n+r) terms is

If the sum of the first 100 terms of an AP is -1 and the sum of even terms lying in first 100 terms is 1 , then which of the following is not true ?

If the arithmetic progression whose common difference is nonzero the sum of first 3n terms is equal to the sum of next n terms. Then, find the ratio of the sum of the 2n terms to the sum of next 2n terms.