Arithmetic Progressions class 10 term-2 A list of numbers in which each term is obtained by adding a fixed number to the preceding term except the first term is called Arithmetic Progressions. This fixed number is called the common difference of the AP .
The common difference is denoted by d and the first term by a.
Then the AP becomes: a, a + d a + 2d, a + 3d, . . ., T1 = a ; T2 = a+ d ; T3 = a +2d ; T4 = a + 3d ……….Tn = a + (n-1)d
So, the nth term an of the AP with first term a and common difference d is given by an = a + (n – 1) d.
So, T2 – T1 = T3 – T2 = . . . = an – a(n – 1) = d.
an is also called the general term of the AP.
If there are m terms in the AP, then am represents the last term which is sometimes also denoted by l
Arithmetic Progressions having finite number of terms is called a finite AP.
Eg. The heights ( in cm ) of some students of a school standing in a queue in the morning assembly are 147 , 148, 149, . . ., 157.
Arithmetic Progressions having (APs) has finite number of terms is called infinite Arithmetic Progressions. Such APs do not have a last term. Eg. The minimum temperatures ( in degree celsius ) recorded for a week in the month of January in a city, arranged in ascending order are – 3.1, – 3.0, – 2.9, – 2.8, – 2.7, – 2.6, – 2.5