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I.            a, a + d, a + 2d, …………….. is an A.P.

First term = a

Common difference = d.

In this A.P. we have –

(i)    nth term, an = a + (n – 1) d.

(ii)        Sum to n terms is given by 



where is the last term.



II.  If a, a1, a2, a3 …., an, b are in A.P. we say that a1, a2, ….., an are the n arithmetic means (A.M.) between a and b.



III.                It is convenient to take :

(i)    Three numbers in A.P. as  (a – d), a, (a + d).

(ii)        Four numbers in A.P. as (a – 3d), (a – d), (a + d), (a + 3d)

(iii)      Five numbers of AP as a – 2d, a–d, a, a + d, a + 2d


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