fourth grade math

From the two examples it is seen that the signs of the terms of a GP must either be all alike or alternatively positive and negative. Note that the numbers in continued proportion are in GP, i.e.,..

If a,b,c,d are in A.P., then (ii) ka, kc, kb, kd are also in A.P. A remark on finding a few members of an A.P. whose sum is given along with other conditions: i) If the sum of three numbers in A.P. is given, take the numbers as a-d, a, a+..

Arithmetic Mean (A.M.) - 1. If a, x, b are in A.P, then x is called the arithmetic mean (A.M.) between the extremes a and b. 2. a. To insert n arithmetic means between two given quantities. Let a and b be any two given quantities, and let A 1 ,A 2 ,A 3 ,-----A n be n arithmetic means to be inserted..

Harmonic Progression (H.P.) - A sequence of numbers is said to form a harmonic progression if their reciprocals form an arithmetic progressio..

Some Properties of A.P. - If a,b,c,d are in A.P., then (ii) ka, kc, kb, kd are also in A.P. A remark on finding a few members of an A.P. whose sum is given along with other conditions: i) If the sum of three numbers in A.P. is given, take the numbers as a-d, a, a+..

Question: Prove that the number of ways in which (m+n) dissimilar things can be divided into two groups containing m and n Answer: If we select m things out of (m+n) things, then n things are left out . Then, this gives (m+n) that can be divided into two groups containing m and n thin..

Question: From a class of 32 students, 4 are to be chosen for a competition. In how many ways can this be done? Answer: We are to select 4 students from 32. This selection can done in ..

Question: A committee of 6 is chosen from 10 men and 7 women so as to contain atleast 3 men and 2 women. In how many different ways can this be done, if two particular women refuse to serve on the same committee? Answer: Let the two ladies who refuse to work on the same committee be d..

Question: Find the number of diagonals in a polygon of n sides. Answer: In a polygon, no three points are collinear. To draw a line, we require two distinct points. The polygon of n sides has n distinct points. Number of diagonals that can be drawn ..

The adjoint of a square matrix [a i j ] is defined as the transpose of the matrix [A i j ] where A i j are the cofactors of the elements a i j . Adjoint of A is denoted by adj A. ..