Terms in a sequence

In a sequence, ordered terms are represented as t₁, t₂, t₃, . . . . .t_n . . . In general sequence is written as {tn}. If the sequence is infinite, for every positive integer n, there is a term t_n.

Activity I : Some sequences are given below. Show the positions of the terms by t₁, t₂, t₃, . . .

(1) 9, 15, 21, 27, . . .     Here t₁= 9,   t₂= 15,   t₃= 21, . . .
(2) 7, 7, 7, 7, . . .           Here t₁= 7,   t2=___ ,  t3= ___, . . .
(3) -2, -6, -10, -14, . . . Here t₁= -2,  t2=___ ,  t3= ___, . . .

Activity II : Some sequences are given below. Check whether there is any rule among the terms. Find the similarity between two sequences.
       To check the rule for the terms of the sequence look at the arrangements on the next page, and fill the empty boxes suitably.

(1) 1, 4, 7, 10, 13, . . .     (2) 6, 12, 18, 24, . . .
(3) 3, 3, 3, 3, . . .             (4) 4, 16, 64, . . .
(5) -1, -1.5, -2, -2.5, . . .  (6) 13, 23, 33, 43, . . .

Let’s find the relation in these sequences. Let’s understand the thought behind it.

     Here in the sequences (1), (2), (3), (5), the similarity is that next term is obtained by adding a particular number to the previous number. Each ot these sequences is called an Arithmetic Progression.
    Sequence (4) is not an arithmetic progression. In this sequence the next term is obtained by mutliplying the  previous term by a particular number. This type of sequences is called a Geometric Progression.
    Sequence (6) is neither arithmetic progression nor geometric progression.