different number patterns

. Pascal's triangle The coefficients of various terms in (a+b) n for different values of n follows the pattern given below: General term For 0 < r < n, T r+1 in the expression of (a + b) n is given by T r+1 = n C r a n-r b r . (r + 1) t h term at the end in the expansion o..

If A and B are two sets, we define their symmetric difference as the set of all elements that belong to A or to B, but not both A and B, and we denote it by A D B. Thu..

Quantities are said to be in Arithmetic progression when they increase or decrease by a common difference..

Factorisation of trinomials of the form x 2 +bx+c - Factorisation of trinomials of the form x 2 +bx+c Trinomials are expressions with three terms. For example, x 2 + 14x + 49 is a trinomial. There is no single method by which all trinomials can be factorised. We need to study the pattern ..

We have seen the application of matrices and determinants in solving system of linear equation with three unknown variables. Matrices and determinants are also widely used in solving large system of linear equation. Some of these methods are Gauss-elimination method, Gauss-Jordan method etc. They a..

Let us consider the marks obtained by four students in Physics, Chemistry and Biology for the first unit test. We have represented the data in rows and columns. (i) Rows show the marks obtained by each student. (ii) The columns show the marks in Physics, Chemistry, Biology obtained by each student...

The Operations on Sets are: Union of sets, Intersection of sets, Disjoint sets, Difference of two sets (Relative complement), Symmetric Difference of two sets, Complement of a se..

Question 1 - Question: For the given sequence, suggest possible next three terms and find the general term. 7, 11, 15,---- Answer: First term = 7, Common Difference = 11 - 7 = 15 - 11 = 4 Next three terms are 15 + 4 = 19, 19 + 4 = 23, 23 + 4 = ..

Difference of two sets A and B, A - B is a set whose elements belong to A but not to B. A - B is called the relative complement of B w.r.t. ..

Let a=first term, d = common difference, l=t n =last term, s = required sum. Then, Writing the series in the reverse order, Adding together the two series, ..