Question

Find the missing term \[9,17,19,27,29,(......),39\]
A) \[38.5\]
B) 38
C) 37
D) \[37.5\]

Answer 1

Hint:
Here we will first find the pattern that is being followed in the series by finding the difference between the corresponding terms of the series. Then by using the same pattern, we will get the value of the missing term of the given series.

Complete step by step solution:
Given series is \[9,17,19,27,29,(......),39\].
Here we will find the pattern which is being followed in the series.
First, we will find the difference between the first and the second term of the given series. Therefore, we get
Difference between the first and the second term \[ = 17 - 9 = 8\]
Now, we will find the difference between the second and the third term of the given series. Therefore, we get
Difference between the second and the third term \[ = 19 - 17 = 2\]
Now, we will find the difference between the third and the fourth term of the given series. Therefore, we get
Difference between the third and the fourth term \[ = 27 - 19 = 8\]
Now, we will find the difference between the fourth and the fifth term of the given series. Therefore, we get
Difference between the fourth and the fifth term \[ = 29 - 27 = 2\]
Therefore, we can clearly see that in the series the number is increasing as \[ + 8, + 2, + 8, + 2,...\].
So, the missing term is \[ = 29 + 8 = 37\]
Hence the missing term in the given series is equal to 37.

So, option C is the correct option.

Note:
Here while finding the missing we have to form the pattern accordingly. If the terms of the values increase in the large amount then the pattern should be in the multiplication form. So, we have to apply the approach for finding the pattern of the series according to the given series. We always have to keep in mind the basic A.P. and G.P series as sometimes simple A.P. or G.P. is applicable to the series of the numbers.