Formulae and Shortcuts - making life easier!
More formulae:
PROGRESSION:
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)
ARITHMETIC PROGRESSION
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
GEOMETRIC PROGRESSION
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
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