#### Formulae and Shortcuts - making life easier!

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, 08-14-2010 at 10:17 PM (1639 Views)
[QUOTE=suja84_ibt;205580]More formulae:

[b]PROGRESSION:

[/b]Sum of first n natural numbers: 1 +2 +3 + .... + n = [n(n+1)]/2

Sum of first n odd numbers: 1 + 3 + 5 + .... upto n terms = n^2

Sum of first n even numbers: 2 + 4 + 6 + ... upto n terms = n(n+1)

[b]

ARITHMETIC PROGRESSION[/b]

nth term of an Arithmetic progression = a + (n-1)d

Sum of n terms in an AP = s = n/2 [2a + (n-1)d]

where, a is the first term and d is the common differnce.

If a, b and c are any three consequtive terms in an AP, then 2b = a + c

[b]

GEOMETRIC PROGRESSION[/b]

nth term of a GP is = a[r^(n-1)]

sum of n terms of a GP:

s = a [(r^n - 1)/(r-1)] if r > 1

s = a [(1 - r^n)/(r-1)] if r < 1]

sum of an infinite number of terms of a GP is

s(approx.) = a/ (1-r) if r <1

If a, b and c are any three consequtive terms in a GP, then b^2 = a + c

PS: Everybody!!! please contribute or this thread will never grow.[/QUOTE]