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Key Points

 

1.  In AP, am+n + am-n = 2 am
 

 

2.  In AP, am = n, an = m then ap = m + n – p

 

3.  In AP, Sp = a, Sq = b, Sr = c, then
 

 

4.  In AP, ap=a, aq = b, ar = c, then a (q–r) + b (r–p) + c (p–q) = 0
 

 

5.  If A and G be A.M and G.M., respectively between two positive numbers x and y then


x =
 

 

6.  If a, b, c and d are in G.P., show that (a2+b2+c2) (b2+c2+d2) = (ab+bc+cd)2
 

 

7.  If pth, qth, rth and sth terms of an A.P. are in G.P. then (p–q), (q–r), (p–q), (q–r), (r–s) are also in G.P.

 

8.  If a, b, c are in G.P and , then x, y, z are in A.P.
 

 

9.  The ratio of the A.M and G.M. of two positive numbers a and b is m : n then
 

a : b =
 

 

10.       In A.P., Sm = n, Sn = m, then Sm+n = – (m+n)
 

 

11.       In A.P., Sm =
 

 

12.       In A.P., am =
 

 





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