Sequences and series
If G is the geometric mean of x and y, then
Assertion :The sum of first n terms of an A.P. whose first term is A, the second term is B and the last term is L, is equal to 2(B−A)(B+L−2A)(A+L)
Reason :If the sim of p terms of an A.P. is equal to the sum of its q terms, then the sum of its (p+q) terms is p+q
If in an A.P. the sum of p terms is equal to sum of q terms, then prove that the sum of p+q terms is zero.
There are two A.P.'s whose common differences differ by unity, but sum of the three consecutive terms in each is 15. If P and P1 be the products of these terms such that P1P=87, then find the common term for all such possible A.P's?
Suppose θ and (ϕ=0) are such that sec(θ+ϕ), secθ and sec(θ−ϕ) are in A.P. If cosθ=kcos(2ϕ) for some k, then k is equal to?