xmath

SEQUENCES

1. A sequence is an ordered arrangement of numbers according to a given rule.

The individual numbers that form a sequence are the terms of a sequence.

Eg: The numbers 1,3,5,7………form a sequence and the individual numbers are called the terms of the sequence.

. A sequence having a finite number of terms is a finite sequence.

a) 4, 8, 12, 16, 20, 28, 32, 36, 40

b) 5, 10, 20 ………………….. 1000

3. A sequence having an infinite number of terms is an infinite sequence.

Eg: a) 3, 9, 27, 81………..

b) 6, 4, 2, 0, -2 ………….

nth term of even natural number = 2n

nth term of odd natural number = 2n-1

Sum of first ‘n’ odd natural numbers = n²

A ≥G ≥ H, A G & H are in G.P

Arithmetic Progression: is a sequence in which the difference between a term and its proceedings terms is a constant

Geometric Progression: is a sequence in which the ration of a term and its proceeding term is constant

Harmonic progression: is a sequence in which the reciprocal of terms of it form an A.P

Points to Ponder

· Ordered arrangement of numbers according given rule is a sequence

Eg: 1) 1, 3, 5, 7………….2) 2, 4, 8, 16…………., ………..

· A sequence having finite number of terms is a finite sequence

· A sequence having infinite number of terms is an infinite sequence

· Series:Sum of the terms of a sequence is the series.

· Arithmetic Progression [A.P]:It is a sequence in which the difference between a term and its preceding term is a constant.

Formulae Related to A. P.

General form: a, a+d, a+2d, ……………

nth term of an A.P. : T_n = a+(n-1)d, T_n = S_n-S_n-1

Mean term: A= a+b/2

Sum of n terms:S_n = n/2[a+1]

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

Σn = n/2[a+l]