NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions
2. Arithmetic Progression : A succession of number is said to be an Arithmetic Progression (AP), if each term of the sequence can be obtained by adding a fixed numbered to the preceding term except the first term a. The fixed numbered may be positive, negative or zero and is called the common difference of AP.
general term of an AP is a, a + d, a + 2d, a + 3d,...
(i) 3, 7, 11, 15, 19, ...
(ii) 15, 12, 9, 6, 3, ...
(iii) 2, 2, 2, 2, ....
(iv) – 2.5, – 3, – 3.5, – 4, – 4.5, ....
Note : A given list of numbers a1, a2, a3 ,..... is an AP, if the difference a2 – a1, a3, give the same value.
3. nth term of an AP : The nth term an (or the general term) of an AP is an = a + (n – 1)d, where a is the first term and d is the common difference.
4. nth term of an AP from the End : The nth term an (or the general term) of an AP from the end an = l – (n – 1)d, where l is the last term and d is the common difference.
5. Sum of n terms of an AP : The sum Sn of the first n terms of an AP is given by
Note : If l is the last term of the finite AP say the nth term, then the sum of all terms of the AP is given by