Sequences and Series

A sequence is an ordered arrangement

A sequence is an ordered arrangement of numbers following a definite pattern. When sequences follow specific mathematical patterns, they are called pr

A sequence where the difference between

A sequence where the difference between consecutive terms is constant. For A.P. with first term 'a' and common difference 'd': nth term = a + (n-1)d,

A sequence where the ratio between

A sequence where the ratio between consecutive terms is constant. For G.P. with first term 'a' and common ratio 'r': nth term = ar^(n-1), Sum of n ter

A sequence where the reciprocals

A sequence where the reciprocals of terms form an A.P. If 1/t₁, 1/t₂, 1/t₃,... are in A.P., then t₁, t₂, t₃,... are in H.P. Example: 1/2, 1/5, 1/8, 1/

For two numbers x and y

For two numbers x and y: A.M. = (x+y)/2, G.M. = √(xy), H.M. = 2xy/(x+y). These satisfy the relationship A.M. ≥ G.M. ≥ H.M., with equality when x=y. Al