Answer
453.3k+ views
Hint: The difference between the terms of the series is in arithmetic progression and that difference is added to the last number.
The given series is: 22, 26, 29, 31,……..
If we observe the terms of the series, it is not in arithmetic, geometric or harmonic progression. However, if we consider the difference between the terms of the series we will get:
4 is the difference between first two terms (i.e. 26-24),
3 is the difference between first two terms (i.e. 29-26),
2 is the difference between the first two terms (i.e. 31-29).
Therefore, the difference between the terms is in A.P. We have 4,3,2… as our difference series. So, its next term is obviously 1. This means that the difference between the next two terms of the initial series is 1. So, if s is the next term of the initial series, we have:
$
\Rightarrow s - 31 = 1, \\
\Rightarrow s = 1 + 31, \\
\Rightarrow s = 32 \\
$
Therefore the next term of the series is 32.
Note: If we observe our difference series, it is in decreasing A.P. If we extend it, we’ll get:
4,3,2,1,0,-1,….
So, after a certain stage its terms will be negative. Which means our initial series will start decreasing as we can see if we follow it:
22,26,29,31,32,32,31,29…..
Thus the series is first increasing and then decreasing.
The given series is: 22, 26, 29, 31,……..
If we observe the terms of the series, it is not in arithmetic, geometric or harmonic progression. However, if we consider the difference between the terms of the series we will get:
4 is the difference between first two terms (i.e. 26-24),
3 is the difference between first two terms (i.e. 29-26),
2 is the difference between the first two terms (i.e. 31-29).
Therefore, the difference between the terms is in A.P. We have 4,3,2… as our difference series. So, its next term is obviously 1. This means that the difference between the next two terms of the initial series is 1. So, if s is the next term of the initial series, we have:
$
\Rightarrow s - 31 = 1, \\
\Rightarrow s = 1 + 31, \\
\Rightarrow s = 32 \\
$
Therefore the next term of the series is 32.
Note: If we observe our difference series, it is in decreasing A.P. If we extend it, we’ll get:
4,3,2,1,0,-1,….
So, after a certain stage its terms will be negative. Which means our initial series will start decreasing as we can see if we follow it:
22,26,29,31,32,32,31,29…..
Thus the series is first increasing and then decreasing.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Why Are Noble Gases NonReactive class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
At which age domestication of animals started A Neolithic class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)