Identify each of the following sequences as finite or infinite.
Problem 1 :
2, 5, 8, 11, 14
Problem 2 :
5, 10, 15, 20, ........, 95
Problem 3 :
Set of first 100 natural numbers
Problem 4 :
Set of prime numbers less than 20
Problem 5 :
The general term of a sequence is tn = n2 + 2n, where
n = 1, 2, 3, ........, 5
Problem 6 :
2, 5, 8, 11, ........
Problem 7 :
5, 10, 15, 20, ........
Problem 8 :
Set of natural numbers
Problem 9 :
Set of whole numbers
Problem 10 :
Set of prime numbers
Problem 11 :
Set of integers
Problem 12 :
The general term of a sequence is tn = n2 + 2n, where n is a natural number.
Since n is a natural number,
n = 1, 2, 3, 4, ........
1. Answer :
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.
2. Answer :
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.
3. Answer :
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.
4. Answer :
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.
5. Answer :
The general term of the sequence is
tn = n2 + 2n
where n = 1, 2, 3, ........, 5.
Substitute n = 1, 2, 3, 4, 5 in tn = 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.
6. Answer :
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.
7. Answer :
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.
8. Answer :
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.
9. Answer :
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.
10. Answer :
Set of prime numbers
We can write the above set as a sequence.
2, 3, 5, 7, 11, 13, ........
The above sequence of prime numbers continues infinitely and no last term. Since the sequence does not have last term, it is an infinite sequence.
11. Answer :
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.
12. Answer :
The general term of the sequence is tn = 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, ........ in tn = 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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