Question

Which one of the following is not true?
A.A sequence is a real valued function defined on N.
B.Every function represents a sequence.
C.A sequence may have infinitely any terms.
D.A sequence may have a finite number of terms.

Answer 1

Hint: Here we will use the basic definition of sequence. We will check for each statement given and check whether the statements are true or not true. Then select the statement which is not true.

Complete step-by-step answer:
From the option, we can observe that all options are related to sequence. So, first we will write the definition of sequence.
We know that the sequence or series is defined as a function whose domain is the set of natural numbers or a subset of the natural numbers.
Hence, we can say that every function represents a sequence which means option B is true.
Also from the definition of the sequence we can say that a sequence can be finite or infinite which means option C and option D are also true.
The only option left is option A which is not true.
Hence, a sequence is a real valued function defined on N is not true.
So, option A is the correct option.

Note: Here we should know the basic definition of sequence. We should have basic types of sequence.
Types of Sequence and Series
Arithmetic Sequences- It is a sequence in which there is a constant common difference between the two consecutive numbers in the series.
Geometric Sequences - It is a sequence in which there is a constant common ratio between the two consecutive numbers in the series.
Harmonic Sequences - It is a series of numbers in which the reciprocals of all the elements of the sequence gives an arithmetic sequence or series.
Fibonacci Numbers - Fibonacci Numbers form an interesting sequence of numbers in which each element is obtained by adding two preceding elements of the series and the sequence always starts with 0 and 1.