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# Find the next term of the series:22, 26, 29, 31,……..(A) 32 (B) 33 (C) 34 (D) 35  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.
View Notes
Table of 29 - Multiplication Table of 29  Determinant to Find the Area of a Triangle  Table of 31 - Multiplication Table of 31  Table of 26 - Multiplication Table of 26  Arithmetic Progression  Table of 22 - Multiplication Table of 22  Elements of the First Transition Series  How to Find The Median?  To Find the Weight of a Given Body Using Parallelogram Law of Vectors  The Making of a Scientist  