# Arithmetic Progression For Class 10

In nature, things like petal of a sunflower, the holes of a honeycomb, the grains on the maize cob, etc. follows a fixed pattern.

An arithmetic progression is a list of numbers in which each term differs from its preceding term by a constant number, except the first term. This fixed number is called as common difference(d) of the A.P. This common difference can be positive, negative or even zero.

nth term of an A.P.-

Consider the series having its first term to be ‘a’ and the common difference to be ‘d,’ then the nth term of the series is given as,

$\mathbf{a_{n} = a+(n-1)d}$

The series is given as $a, a+d, a+2d,…………, a+(n-1)d$

Sum of n terms of an A.P.-

The sum of n terms of an A.P. is given as-

$\mathbf{S_{n} = \frac{n}{2} \left ( 2a + (n-1)d \right )}$

Or, $S_{n} = \frac{n}{2} \left ( a + a + (n-1)d \right ) = \frac{n}{2} \left ( a + a_{n} \right )$,

where $a_{n}$ is the nth term of an A.P.

#### Practise This Question

If D,E,F are respectively the mid points of the sides BC , CA and AB of ABC and

the area of ABC is 24 sq. cm, then the area of DEF is -