IIT JEE , AIEEE Forum - Articles Category , Community shelf

apoorva_43

CRAM TO MEMORY TIPS IN SEQUENCE N SERIES

1) If aⁿ⁺¹+ bⁿ⁺¹/aⁿ + bⁿ is AM b/w a and b then n=0, GM b/w a and b then n=-1/2, HM b/w a and b then n=-1

2) If x, y, z are the p^th , q^th, r^th terms of an AP n GP then x^y-z.y^{z- x}.z^x-y=1

3) If a, b,c in GP then log_a^m, log_b^m , log_c^m in HP and vice-versa

4) If in a triangleABC; cotA, cotB, cotC are in AP, then a²,b²,c² are in AP

5) If a,b,c be sides of tr.ABC and r₁,r₂,r₃ be ex-radii of the circles drawn on sides opposite to the angles ; then if a,b,c in AP then r₁,r₂,r₃ in HP n vice-versa

6) If m^th term of HP=n, n^th term of HP=m then (m+n)^th term of HP=mn/m+n and (mn)^th term of HP=1

7) If mth term of AP =1/n , nth term of AP=1/m then (mn)^th term=1 and (m+n)^th term=m+n/mn

8) If (m+n)^th term of GP=p , (m-n)^th term of GP=q then mth term=(pq)^1/2and n^th term=p(q/p)^m/2n

hope this is useful.....

Community Contributions - Articles by goIITians