CBSE Class 10 Math, Quadratic Equations

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.

•   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