Class X Math
Notes for Arithmetic Progression
A group of numbers connected by a definite law is known as sequence.
Arithmetic Progression
A Sequence in which each term is obtained from the preceeding term by adding a constant quantity to it.
A sequence is called a series if its terms are connected by the sign of addition or subtraction.
nth term of an Arithmetic Progression
an = a + (n - 1) d = l
where a is first term and d is common difference l is last term.
Selection of terms of an A.P.
When odd number of terms are required. Take middle term as ‘a’ and common difference as ‘d’.
When even number of terms are required take a - d, a + d as two middle terms and ‘2d’ as common difference.
The condition for three terms to be in an Arithmetic Progression is that common difference between them must be same.
⇒      t3t2 = t2t1
Sum of n terms of an A.P. l is the last term
a is the first term
d is the common difference
nth term from the end is l - (n - 1)d.
where l is last term, d is common difference.
The Standard form of an Arithmetic Progression is
a + (a + d) + (a + 2d) + .... (l - d) + l
a is first term, l is last term, d is common difference
nth term of an Arithmetic Progression is the difference of the sum to first n terms and the sum to first (n - 1) terms
an = Sn - Sn - 1