Which sequence is a reciprocal of arithmetic sequence?
1.Fibonacci sequence
2.Harmonic sequence
3.Arithmetic sequence
4.Geometric sequence
Answer
627.6k+ views
Hint: Here we will use the concept of arithmetic progression to answer the question. We will then compare the definition of given terms in the option with that of arithmetic series. The term that has formed a series having reciprocal terms in arithmetic sequence will be the required answer.
Complete step-by-step answer:
Here we need to determine the sequence which will be the reciprocal of the arithmetic sequence.
We know that a sequence is defined as the group of numbers which follows a particular pattern. An arithmetic sequence is defined as the sequence in which the difference between any two consecutive terms is a constant.
Now we will analyze the definition of terms given in the option.
We know that Fibonacci sequence is a series or sequence in which every number is a sum of the last two terms.
A harmonic sequence is defined as the sequence of real numbers which is formed by taking the reciprocal of an arithmetic progression.
Now, a geometric sequence is a series in which the consecutive terms have a common ratio.
Now by looking at all the definitions, we can say that the harmonic sequence is the required sequence which is reciprocal of arithmetic sequence.
Hence, the correct option is option C.
Note: Here we have obtained that the harmonic sequence is the required sequence which is reciprocal of arithmetic sequence. Some important properties of arithmetic sequence or arithmetic progression are as follows:
1. If we add or subtract a number from each term of the arithmetic progression, then the resulting terms in the sequence are also in AP.
2. If we multiply or divide a number from each term of the arithmetic progression, then the resulting terms in the sequence are also in AP.
Complete step-by-step answer:
Here we need to determine the sequence which will be the reciprocal of the arithmetic sequence.
We know that a sequence is defined as the group of numbers which follows a particular pattern. An arithmetic sequence is defined as the sequence in which the difference between any two consecutive terms is a constant.
Now we will analyze the definition of terms given in the option.
We know that Fibonacci sequence is a series or sequence in which every number is a sum of the last two terms.
A harmonic sequence is defined as the sequence of real numbers which is formed by taking the reciprocal of an arithmetic progression.
Now, a geometric sequence is a series in which the consecutive terms have a common ratio.
Now by looking at all the definitions, we can say that the harmonic sequence is the required sequence which is reciprocal of arithmetic sequence.
Hence, the correct option is option C.
Note: Here we have obtained that the harmonic sequence is the required sequence which is reciprocal of arithmetic sequence. Some important properties of arithmetic sequence or arithmetic progression are as follows:
1. If we add or subtract a number from each term of the arithmetic progression, then the resulting terms in the sequence are also in AP.
2. If we multiply or divide a number from each term of the arithmetic progression, then the resulting terms in the sequence are also in AP.
Recently Updated Pages
Write any three differences between metals and nonmetals class 10 social science CBSE

Amit standing on a horizontal plane finds a bird flying class 10 maths CBSE

Two circles of radii 5 cm and 3 cm intersect at two class 10 maths CBSE

Solve the following i John and Jivanti together have class 10 maths CBSE

What is the relation between orthocenter circumcentre class 10 maths CBSE

Two plane mirrors are inclined at 70circ A ray incident class 10 physics CBSE

Trending doubts
Explain the Treaty of Vienna of 1815 class 10 social science CBSE

Which country is known as "The land of Fire and Ice"?

1 GB equals how many MB?

10 examples of evaporation in daily life with explanations

What is the full form of POSCO class 10 social science CBSE

Which is the hottest planet in the Solar system A Earth class 10 social science CBSE

