Class X Math
Notes for Arithmetic Progression
A group of numbers connected by a definite law is known as sequence.
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.
⇒ t3 ‐ t2 = t2 – t1
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