7,9,13,21,40,69,133

To find the wrong number and form a new series, we need to analyze the pattern in the given series. Let's break down the series and identify the pattern:

Original Series:
7, 9, 13, 21, 40, 69, 133

Step 1: Find the Differences:
To identify the pattern, we can start by finding the differences between consecutive terms in the series.

9 - 7 = 2
13 - 9 = 4
21 - 13 = 8
40 - 21 = 19
69 - 40 = 29
133 - 69 = 64

Step 2: Find the Second Differences:
Now, let's find the differences between consecutive differences.

4 - 2 = 2
8 - 4 = 4
19 - 8 = 11
29 - 19 = 10
64 - 29 = 35

Step 3: Analyze the Second Differences:
From the second differences, we can observe that the values are not constant. Therefore, the pattern in the given series is not linear.

New Series:
To form a new series, we can consider the first few terms and observe any alternate patterns.

7, 9, 13, 21

From the original series, we can see that the terms are increasing but not in a consistent manner.

Step 4: Forming the New Series:
Let's create a new series by considering the sum of the previous two terms of the original series.

7 + 9 = 16
9 + 13 = 22
13 + 21 = 34
21 + 40 = 61
40 + 69 = 109
69 + 133 = 202

New Series:
16, 22, 34, 61, 109, 202

Finding the Fifth Term:
To find the fifth term in the new series, we can observe that the pattern in the new series is now increasing in a consistent manner.

Therefore, the fifth term in the new series is 109.

Explanation:
By analyzing the pattern in the original series and forming a new series based on the sum of previous terms, we were able to identify the fifth term in the new series as 109.

Given, 7,9,13,21,40,69,133.
now, First series 7 , 13(7×2 -1), 40(13×3+1), 133(wrong 40×4-1=159) 2nd series 9, 21(9×2+3), 69(21×3+3).