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

If three quantities are in harmonic progression, then the middle quantity is called the harmonic mean between the other two. Example: 1/3, 1/7, 1/11 are in H.P., then 1/7 is the middle term. Hence 1/7 is the harmonic mean between 1/3 and 1/1..

A sequence of numbers is said to form a harmonic progression if their reciprocals form an arithmetic progressio..

To find the n t h term of an H.P, find the n t h term of the corresponding A.P. obtained by the reciprocals of the terms of the given H.P. Now the reciprocal of the n t h term of an A.P. will be the n t h term of the H.P..

Let |aij| be a determinant of order n. The determinant obtained by deleting the i t h row and j t h column in which the element a i j lies is called the minor of element a i j and is denoted by M i ..

Let H be the harmonic mean between the quantities a and b. ..

Let a and b be two given quantities. It is required to insert n harmonic means h 1 , h 2 , h 3 ,....h n between the quantities a and b. Let d = common difference of the A.P. Hence h 1 , h 2 ,....h..

A square matrix A = [a i j ] is said to be symmetric if its (i,j) t h element is the same as its (j,i) t h element. i.e a i j = a j i " i, j A square matrix A is said to be symmetric, if A = A ..

) A sequence may be described by giving a formula for its n t h term. (iii) A sequence may be described by specifying its first few terms and a formula to determine the other terms of the sequence in terms of its proceeding terms. A sequence is said to be a progression if its terms numeri..

Consider the arrangement In this arrangement, there are two rows and four columns. The number 3 lies in the 2 n d row and 4 t h column. Each number has a fixed position. Matrix A has 2 rows and 3 columns and is thus of order 2 x 3. Matrix B has 3 rows and 2 columns and is thus of order 3 ..