The sequence 6, 12, 24, 48, 96 is a finite sequence of five terms. Can you think of other finite sequences that you see in your daily life?
Step-by-step solution
Idea: A sequence is finite if it has a last term, so it has a fixed number of terms. Anything we can list in order that stops somewhere is a finite sequence.
- A finite sequence is an ordered list that ends. The given sequence 6, 12, 24, 48, 96 stops after 5 terms.½ mark
- Dates of September: 1, 2, 3, …, 30. It has 30 terms; the last term is 30.½ mark
- Roll numbers in a class of 40 students: 1, 2, 3, …, 40. Floor numbers of a 12-storey building: 0, 1, 2, …, 11.½ mark
- Bus fares on a route, or the runs at the end of each over in a 20-over innings (20 terms, e.g. 8, 15, 21, …). Each list stops, so each is finite.½ mark
Answer to write in the exam
A finite sequence has a last term.
Dates of September: 1, 2, 3, …, 30 (30 terms)
Roll numbers of a class of 40: 1, 2, …, 40
Floors of a 12-storey building: 0, 1, 2, …, 11
∴ These are finite sequences from daily life.
Common mistakes that cost marks
- Giving ‘all the even numbers’ as a finite sequence. It never stops, so it is infinite.
- Giving a set with no order, such as ‘the students in my class’. A sequence needs an order: first, second, third, …
- Thinking a finite sequence must be short. 1, 2, 3, …, 1000 is finite too, because it has a last term.
How this can come in the exam
Which of these is a finite sequence?
- 1, 2, 3, 4, …
- 2, 4, 6, 8, …
- 1, 2, 3, …, 31 (dates of January)
- 1, 4, 9, 16, …
Show answer
(C) 1, 2, 3, …, 31 (dates of January)
The dates of January stop at 31, so that list has a last term. The other three go on forever.
Try one yourself
Is the list of all two-digit multiples of 10 (10, 20, …, 90) a finite or an infinite sequence? How many terms does it have?
Show answer
It is finite: it stops at 90. It has 9 terms (10, 20, 30, 40, 50, 60, 70, 80, 90).
More questions like this
- Each term of the triangular number sequence is the sum of the natural numbers up to that term. For example, 15, the fifth triangular number, is equal to 1 + 2 + 3 + 4 + 5. This is represented by the diagram in the figure, where each triangular number is represented by a triangular array of dots. Can you draw the patterns for the next two terms of the sequence?
- 1 = 1, 4 = 1 + 3, 9 = 1 + 3 + 5, 16 = 1 + 3 + 5 + 7, and so on. Each term in the square number sequence is the sum of the odd numbers up to that term. This interesting relationship between the odd numbers and square numbers can be represented by the diagram in the figure. Can you explain the relationship?
- Consider the sequence 1, 4, 7, 10, 13, … Can you predict the next four terms? Can you derive the first 10 terms of the sequence obtained by adding all the terms up to a given term of this sequence? (Hint: The first term is 1. The second term is 1 + 4 = 5, the third term is 1 + 4 + 7 = 12, and so on.)
- Can you write t5, t6, t7 and t8 for the sequence of triangular numbers?
- Can you think of any other kinds of sequences? List out five different types of sequences and discuss their properties with your friends.
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