FINITE AND INFINITE SEQUENCES

Example 1 :

2, 5, 8, 11, 14

In the sequence above, the first term is 4 and the last term is 14. Since the sequence has a last term, it is a finite sequence.

Example 2 :

5, 10, 15, 20, ........, 95

In the sequence above, the first term is 5 and the last term is 95. Since the sequence has a last term, it is a finite sequence.

Example 3 :

Set of first 100 natural numbers

We can write the above set as a sequence.

1, 2, 3, ........, 100

In the sequence above, the first term is 1 and the last term is 100. Since the sequence has a last term, it is a finite sequence.

Example 4 :

Set of prime numbers less than 20

We can write the above set as a sequence.

2, 3, 5, 7, 11, 13, 17, 19

In the sequence above, the first term is 2 and the last term is 19. Since the sequence has a last term, it is a finite sequence.

Example 5 :

The general term of a sequence is t_n = n² + 2n, where 

n = 1, 2, 3, ........, 5 

Substitute n = 1, 2, 3, 4, 5 in t_n = n² + 2n.

t₁ = 1² + 2(1) = 1 + 2 = 3

t₂ = 2² + 2(2) = 4 + 4 = 8

t₃ = 3² + 2(3) = 9 + 6 = 15

t₄ = 4² + 2(4) = 16 + 8 = 24

t₅ = 5² + 2(5) = 25 + 10 = 35

The sequence is

3, 8, 15, 24, 35

In the sequence above, the first term is 3 and the last term is 35. Since the sequence has a last term, it is a finite sequence.

Example 6 :

2, 5, 8, 11, ........

In the sequence above, after the four terms shown, it continues infinitely and no last tern. Since the sequence does not have a last term, it is an infinite sequence.

Example 7 :

5, 10, 15, 20, ........

In the sequence above, after the four terms shown, it continues infinitely and no last tern. Since the sequence does not have a last term, it is an infinite sequence.

Example 8 :

Set of natural numbers

We can write the above set as a sequence.

1, 2, 3, 4, ........

The above sequence of natural numbers continues infinitely and no last term. Since the sequence does not have last term, it is an infinite sequence.

Example 9 :

Set of whole numbers

We can write the above set as a sequence.

0, 1, 2, 3, 4, ........

The above sequence of whole numbers continues infinitely and no last term. Since the sequence does not have last term, it is an infinite sequence.

Example 10 :

Set of whole numbers

We can write the above set as a sequence.

0, 1, 2, 3, 4, ........

The above sequence of whole numbers continues infinitely and no last term. Since the sequence does not have last term, it is an infinite sequence.

Example 11 :

Set of integers

We can write the above set as a sequence.

........, -3, -2, -1, 0, 1, 2, 3, ........

The above sequence of integers continues infinitely and no last term. Since the sequence does not have last term, it is an infinite sequence.

Example 12 :

The general term of a sequence is t_n = n² + 2n, where n is a natural number.

Since n is a natural number,

n = 1, 2, 3, 4, ........

Substitute n = 1, 2, 3, 4, ........ t_n = n² + 2n.

t₁ = 1² + 2(1) = 1 + 2 = 3

t₂ = 2² + 2(2) = 4 + 4 = 8

t₃ = 3² + 2(3) = 9 + 6 = 15

t₄ = 4² + 2(4) = 16 + 8 = 24

The sequence is

3, 8, 15, 24, ........

In the sequence above, after the four terms shown, it continues infinitely and no last tern. Since the sequence does not have a last term, it is an infinite sequence.

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