Psc Cracker

Arithmetic progression (AP) is a sequence of numbers satisfying the condition that the difference between any two consecutive numbers is constant If the first term is denoted as ‘a’ The common difference as ‘d’ The number of terms as n.   Then nth term is a n = a + (n – 1)d. Sum of n terms, Sn = n/2 [2a + (n - 1) d] = n/2 (first term + last term). Sum of the first n natural numbers 1 + 2 + 3 + … + n = n(n+1)/2 Sum of squares of the first n natural numbers 1 2 + 2²+ 3²+ …. + n² = n(n + 1)(2n + 1)/6 Sum of cubes of first n natural numbers 1³+ 2³ + 3³ + …+ n³ = (1 + 2 + 3 + …+ n)² = [ n(n + 1)/2]² Sum of the first n odd numbers 1 + 3 + … + (2n – 1) = n² Sum of the first n even numbers 2+4+...+2n= n(n+1) If a,b,c are three consecutive terms of an AP then 2b=a+c Geometric progression (GP) is a sequence of  terms in which each succeeding term is obtained by multiplying its preceding term by a constant If first ...