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AP

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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