What is the value of x? 4 8 24 32
The Correct Answer and Explanation is:
To determine the value of x in the sequence:
4, 8, 24, 32, x
We first analyze the pattern. The goal is to find a rule or consistent mathematical relationship between the numbers.
Step 1: Observe the Differences
Let’s look at the differences between consecutive terms:
- 8 − 4 = 4
- 24 − 8 = 16
- 32 − 24 = 8
This doesn’t show a clear arithmetic pattern. So let’s try multiplication.
Step 2: Consider Multiplication Patterns
From 4 to 8:
4 × 2 = 8
From 8 to 24:
8 × 3 = 24
From 24 to 32:
24 + 8 = 32 (This breaks the × pattern)
This suggests a possible alternating pattern: one step involves multiplication, the next involves addition.
Step 3: Hypothesis – Alternating Multiply and Add Pattern
Let’s test a pattern of alternating × and +:
- 4 × 2 = 8
- 8 × 3 = 24
- 24 + 8 = 32
- 32 × 1 = 32 (but this doesn’t grow…)
Maybe it’s:
- 4 × 2 = 8
- 8 × 3 = 24
- 24 + 8 = 32
- 32 × 2 = 64 (makes more sense)
Let’s verify the full logic:
- Start with 4
- × 2 → 8
- × 3 → 24
- 8 → 32
- × 2 → 64
✅ So, x = 64
Explanation:
To find the missing value x in the number sequence: 4, 8, 24, 32, x — we need to detect a logical or mathematical pattern that explains how one number transforms into the next. At first glance, the numbers don’t increase linearly, so an arithmetic pattern is unlikely. The differences (4, 16, 8) don’t follow a clear trend either, so the pattern is probably nonlinear, involving multiplication or alternating operations.
Upon closer inspection, the sequence appears to follow a pattern where the rule changes alternately. Specifically:
- The first two numbers follow the rule: 4 × 2 = 8
- The next step: 8 × 3 = 24
- Then the operation changes from multiplication to addition: 24 + 8 = 32
This reveals a potential alternating pattern: multiply, multiply, add, then repeat. The addition of 8 might be a fixed operation. Continuing this pattern:
- After 24 + 8 = 32, we go back to multiplication.
- Next step: 32 × 2 = 64
So, the sequence becomes:
4 → ×2 → 8 → ×3 → 24 → +8 → 32 → ×2 → 64
Thus, the missing value x = 64.
Recognizing alternating patterns like this is a common trick in number sequences. It requires testing a few hypotheses and checking consistency across terms. Such problems often appear in IQ tests, competitive exams, and logic puzzles, training the brain to think algorithmically and spot hidden rules.
