Question

Select the number from the given options that can replace the question mark (?) in the following series.
4, 11, 26, ?, 120, 247

• A. 48
• B. 57
• C. 84
• D. 42

Hint:

When a series grows quickly but not exponentially, test patterns like "multiply by a constant and add/subtract a changing number" (e.g., \(ax+b\), where \(b\) changes arithmetically).

Answer 1

The Correct Option is B

Strategy:

We are given a sequence of numbers with one missing term. We need to find the pattern governing the series to determine the missing number.

There are several ways to find the pattern. We can check the difference between consecutive terms (first-level difference), the difference of the differences (second-level difference), or look for a pattern involving multiplication and addition/subtraction.

Let's try the multiplication and addition approach, as the numbers are increasing quite rapidly.


To get from 4 to 11: \(4 \times 2 + 3 = 8 + 3 = 11\)
To get from 11 to 26: \(11 \times 2 + 4 = 22 + 4 = 26\)
A clear pattern emerges: To get the next term, multiply the current term by 2 and add a number that increases by 1 each time.
The pattern is \(T_n = T_{n-1} \times 2 + (n+1)\), where \(T_1 = 4\).
Let's apply this pattern to find the missing term (?):


The missing term is the 4th term in the series. It is obtained from the 3rd term (26).
Following the pattern, we should multiply by 2 and add 5.
Missing term = \(26 \times 2 + 5 = 52 + 5 = 57\)
So the missing term is 57.
Let's verify the pattern with the rest of the series:


From 57 to 120: \(57 \times 2 + 6 = 114 + 6 = 120\). This matches.
From 120 to 247: \(120 \times 2 + 7 = 240 + 7 = 247\). This also matches.
The pattern is consistent throughout the series.

The number that replaces the question mark is 57.