Determine whether the given sequence is an A.P. 9,16,23,30, …
Answer
282k+ views
Hint: In the given question, we are given a sequence of numbers and we need to find whether it forms an arithmetic progression or not. So, in order to check that we need to use the concept of common difference between the terms of the sequence and hence conclude whether it is an arithmetic progression or not.
Complete step-by-step solution:
In the given question, in order to check whether it is an AP or not we need to use the concept of common difference. By common difference we mean the difference between the two consecutive terms. Now, if this difference between two consecutive terms comes out to be the same then we can say that the given sequence of numbers forms an arithmetic progression.
Now, we are given the numbers of the sequence as 9,16,23,30, …
Here, first term is a=9
And second term is 16
So, the difference between two terms is $16-9=7$ ,
Similarly, the difference between next two terms is $23-16=7$ ,
Similarly, the difference between next two terms is $30-23=7$ .
So, clearly, we can see that the difference between the two consecutive terms is the same. Therefore, we can say that the given sequence forms an arithmetic progression.
Note: In this question we need to be careful and be clear with the concept of geometric progression and arithmetic progression and also, we can be asked to find the next terms of the sequence which we can easily find as we know the common difference if it is an arithmetic progression.
Complete step-by-step solution:
In the given question, in order to check whether it is an AP or not we need to use the concept of common difference. By common difference we mean the difference between the two consecutive terms. Now, if this difference between two consecutive terms comes out to be the same then we can say that the given sequence of numbers forms an arithmetic progression.
Now, we are given the numbers of the sequence as 9,16,23,30, …
Here, first term is a=9
And second term is 16
So, the difference between two terms is $16-9=7$ ,
Similarly, the difference between next two terms is $23-16=7$ ,
Similarly, the difference between next two terms is $30-23=7$ .
So, clearly, we can see that the difference between the two consecutive terms is the same. Therefore, we can say that the given sequence forms an arithmetic progression.
Note: In this question we need to be careful and be clear with the concept of geometric progression and arithmetic progression and also, we can be asked to find the next terms of the sequence which we can easily find as we know the common difference if it is an arithmetic progression.
Recently Updated Pages
Define absolute refractive index of a medium

Find out what do the algal bloom and redtides sign class 10 biology CBSE

Prove that the function fleft x right xn is continuous class 12 maths CBSE

Find the values of other five trigonometric functions class 10 maths CBSE

Find the values of other five trigonometric ratios class 10 maths CBSE

Find the values of other five trigonometric functions class 10 maths CBSE

Trending doubts
Change the following sentences into negative and interrogative class 10 english CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

What is 1 divided by 0 class 8 maths CBSE

Difference Between Plant Cell and Animal Cell

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Convert compound sentence to simple sentence He is class 10 english CBSE

India lies between latitudes and longitudes class 12 social science CBSE

Why are rivers important for the countrys economy class 12 social science CBSE

Distinguish between Khadar and Bhangar class 9 social science CBSE
