## Sequence-III

Examples:

1.  Find the nth term of the sequence:

5, 12, 19, 26, 33, .....

Solution:

Here t₁ = 5

t₂ = 12

t₃ =  19

t₄ = 26, .....

Common difference : d  =  t₄ - t₃ = t₃ - t₂ = t₂ - t

26 - 19 = 19 - 12 = 12 - 5

7    =       7     =    7

So each term is increased by 7. So 7n will come in the formula.

7n sequence :  7, 14, 21, 28, 35, .....

Given sequence: 5, 12, 19, 26, 33, ....

So the nth term of the sequence is 7n-2.

2. Find the nth term of the sequence:

2, 8, 14, 20, 26, .....

Solution:

t₁ = 2, t₂ = 8, t₃ = 14, t₄ = 20

Common difference

d   =   t₄ - t₃ = t₃ - t₂ = t₂ - t

d   =   20 - 14 = 14 - 8 = 8 - 2 = 6

Here each term is increased by 6.  So 6n come in the formula.

6n sequence :        6, 12, 18, 24, 30, ........

Given sequence :   2,  8,   14, 20,  26, ......

So each term in the above sequences is differed by  4.

6 -         12 -       18 - 4     24 - 4    30 - 4

∣                 ∣                 ∣             ∣             ∣

2                            14         20       26

So the nth term of the sequence is 6n - 4.

Find the nth terms of the following sequences.

1.    3, 10, 17, 24, 31, .....
2.    7, 16, 25, 34, 43, ...
3.   4, 14, 24, 34, 44, ....

Students can try to do the problems on their own and become master in finding the nth term of the given sequences.  They can follow the examples we discussed above.  We had given answers for these 3 problems.  Students can verify their answers, with the answers given.  If you are having any doubt, you can contact us through mail, we will help you to clear your doubts.