Arithmetic progression class 10 notes i.e. for chapter 5 provided here are an extremely crucial resource for the students studying in class 10. Chapter 5 notes are not only helpful to study the concepts in an efficient way but are also handy during the revision stage. The following topics are included in the notes given here-

- What is an arithmetic progression
- nth term of an AP
- Sum of n terms of an AP
- Practice Questions

## What is an Arithmetic Progressions (AP)

An arithmetic progression or AP 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 known as the common difference(d) of the A.P. This common difference can be positive, negative or even zero.

### nth term of an Arithmetic Progression (AP)

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.

**Notes: **

- If “l” is the last term of the finite AP, say the nth term, then the sum of all terms of the AP

is given by \(\frac{n}{2}\left ( a+l \right )\) - If a, b, c are in AP, then b = a( + c)/2 and b is called the arithmetic mean of a and c.

### Practice Questions

- Calculate the sum of the first 12 multiples of 13?
- Calculate the number of terms of the AP: 9, 17, 25, . . . which must be taken to get a sum of 636?
- Which term of the following AP is its first negative term? [AP = 121, 117, 113, . . ., ]

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