Complete the following series. 9, 11, 15, 23, 39, $x$

### Concept & Logic Calculate the differences between consecutive numbers. If they form a geometric progression (like powers of 2), apply the next term in that progression. ### Step-by-Step Solution 1. Calculate the first-level differences between the given terms: $11 - 9 = 2$ $15 - 11 = 4$ $23 - 15 = 8$ $39 - 23 = 16$ 2. Observe the sequence of differences: $2, 4, 8, 16$. 3. These differences are successive powers of $2$: $2^1, 2^2, 2^3, 2^4$. 4. The next difference in this sequence must be $2^5 = 32$. 5. Add this difference to the last known term to find $x$: $x = 39 + 32 = 71$. ### Exam Strategy & Shortcut Whenever a series grows slowly but accelerates, immediately write down the differences. Recognizing $2, 4, 8, 16$ takes less than a second, leading instantly to the $+32$ step. ### Common Pitfall Mistaking the powers of $2$ sequence ($2, 4, 8, 16, 32$) for an even numbers sequence or a multiple of differences sequence and adding the wrong value. ### Final Answer Therefore, the correct answer is **71**.