Sequence & Series Formulas

Arithmatic Progression

a,a+d,a+2d...., a+nd

• nth term of arithmatic progression
  

Tn = a + (n-1) d

• Sum of n - terms of arithmatic progression
  

Sn= (n/2) [ 2a + (n - 1) d]

• if a,b and c are in arithmatic progression then b = (a + c)/2.

Geomatric Progression

a,ar,ar^2,..., ar^n

• nth term of geomatric progression is given by Tn = a r^(n-1).
• Sum of the first n terms of geomatric progression is given by;

Sn = a [ (1 - r^n) / (1 - r) ] , for r<1>

Sn = a [ (r^n - 1)/ (r - 1) ], for r>1

• if three quantities a,b and c are in GM then b = Sqrt(ac);
• Infinite Geomatric Series

when |r|<1   

S* = a / (1 - r);

when |r|>1 then 

S*= Infinity;

Harmonic Mean

• HM of a and b is 2ab/(a+b).
• nth terms of Harmonic Progression is  Tn = 1 / [ a + (n-1) d ]

Other Important Formulas

• Sum of first n - natural number is given by:  summation (r=1 to n)  : n (n + 1) / 2.
• Sum of squares of first n - natural number is given by summation (r=1 to n) :[ n ( n + 1 ) (2n + 1)  ] / 6 
• Sum of cubes of first n - natural number is given by summation (r=1 to n) : [n^2 (n+1)^2 ]

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