Arithmetical Progression (A.P.):

• The general form of an A. P. is a, a + d, a + 2d, a + 3d,..... 

• where a is the first term and d, the common difference of the A.P. 

• The nth term of the above A.P. is t₀ = a + (n - 1)d. 

• The sum of first n terns of the above A.P. is s = n/2 (a + l) = (No. of terms/2)[1st term + last term] or, S = ⁿ/₂ [2a + (n - 1) d] 

• The arithmetic mean between two given numbers a and b is (a + b)/2. 

• 1 + 2 + 3 + ...... + n = [n(n + 1)]/2. 

• 1² + 2² + 3² +……………. + n² = [n(n+ 1)(2n+ 1)]/6. 

• 1³ + 2³ + 3³ + . . . . + n³ = [{n(n + 1)}/2 ]².