Question

Which sequence is a reciprocal of arithmetic sequence?
1.Fibonacci sequence
2.Harmonic sequence
3.Arithmetic sequence
4.Geometric sequence

Answer 1

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.