**1.** Some numbers arranged in a definite order, according to a definite rule, are said to form a sequence.

**2.** A sequence is called an arithmetic progression (AP), if the difference of any of its terms and the preceding term is always the same i.e., constant.

**3. **The constant number is called the common difference of the A.P.

**4.** If a is the first term and d is the common difference of an AP, then the general form of the AP is a, a + d, a + 2d, …

**5.** Let a be the first term and d be the common difference of an AP, then, its nth term or general term is given by

**6.** If l is the last term of the AP, then nth term from the end is the nth term of an AP, whose first term is l and common difference is – d nth term from the end = Last term + (n – 1) (– d)

nth term from the end = l – (n – 1) d

**7.** If are in AP, then

(i) are in AP.

(ii) are in AP.

(iii) are in AP.

(iv) are in AP

**8.** Remember the following while working with consecutive terms in an AP.

(i) Three consecutive terms in an AP.

a –d, a, a + d

First term = a – d, common difference = d

Their sum = a – d + a + a + d = 3a

(ii) Four consecutive terms in an AP

a – 3d, a – d, a + d, a + 3d

First term : a – 3d, common difference = 2d

Their sum = a – 3d + a – d + a + d + a + 3d = 4a

(iii) Five consecutive terms in an AP.

a – 2d, a – d, a, a + d, a + 2d

First term = a – 2d, common difference = d

**9.** The sum up to n terms of an AP whose first term is a and common difference d is given by

**10.** If the first term and the last term of an AP are and , then

(first term + last term)

If , the first term and , the last term, then

**11.**

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