Worksheet 10th Class – Maths chapter- Arithmetic progressions
1. Key terms: Arithmetic progression (A.P.) :- An A.P. is a list of numbers in which each term is obtained by adding a fixed number to the preceding term except the first term. This fixed number is called the common difference of the A.P. If a is first term and d is common difference of an A.P. , then the A.P is a , a +d , a+2d , 2+3d ….. The term of an a.p is denoted by and = a+(n-1) d , where a = first term and d = common difference. term from the end = l – (n-1) d , where l = last term. Three terms a-d , a , a+d are in A.P with common difference d. Four terms a-3d , a-d , a+d ,a+3d are in A.P with common diff. 2d . The sum of first n natural number is The sum of n terms of an A.P with first term a and common difference d is denoted by = { 2a+(n-1) d } also , = (a+l) where , l = last term. = - . Where = term of an A.P D = - . Where d = common difference of an A.P. 2. Let us denote the first term of an AP by a1, second term by a2 , . . ., nth t...