Sequence and Series Flashcards
General term of the arithmetic progression
an = a+(n-1)d
Sum of terms in AP
sn = n/2{2a + (n-1)d}
3 no. in AP
a-d, a, a+d
4 no. in AP
a-3d, a-d, a+d, a+3d
5 no. in AP
a-2d, a-d, a, a+d, a+2d
Arithmetic Mean of two numbers
a+b/2
General term of the GP
ar^(n-1)
3 no. in GP
a/r, a, ar
4 no. in GP
a/r^3, a/r, ar, ar^3
5 no. in GP
a/r^2, a/r, a, ar, ar^2
Sum of terms in a finite GP
a(1-r^n)/(1-r)
Sum of terms in an infinite GP
a/1-r
Geometric Mean of two numbers
root a*b
Harmonic Mean of two numbers
2ab/a+b
Relation between A.M., G.M. and H.M.
A.M.*H.M. = (G.M.)^2
AM, GM, and HM inequality
A.M.≥G.M.≥H.M.
Sum of first ‘n’ natural numbers
n(n+1)/2
Sum of squares of first ‘n’ natural numbers
n(n+1)(2n+1)/6
Sum of cubes of first ‘n’ natural numbers
[n(n+1)/2]^2
Sum of first ‘n’ odd numbers
n^2
Sum of first ‘n’ even numbers
n(n+1)
