Consider the following number series: 1, 3, 7, 15, 31, ?.... Identify the…
2023
Consider the following number series: 1, 3, 7, 15, 31, ?....
Identify the missing number (?) from the options given below:
- A.
42
- B.
52
- C.
62
- D.
63
Attempted by 100 students.
Show answer & explanation
Correct answer: D
To find the missing number, observe the pattern in the series: 1, 3, 7, 15, 31. Calculate the difference between consecutive terms: 3 - 1 = 2, 7 - 3 = 4, 15 - 7 = 8, 31 - 15 = 16. These differences are powers of 2 (2, 4, 8, 16). The next difference should be 32. Adding this to the last term: 31 + 32 = 63. Alternatively, each term is double the previous term plus one (n * 2 + 1). Thus, 31 * 2 + 1 = 63.