Question

Complete the series: 7, 10, 16, 28, 52, (?)

• A. 88
• B. 96
• C. 100
• D. 104

Hint:

When solving number series:

• First check the \textbf{differences between consecutive terms}.
• Look for patterns such as doubling, squares, cubes, or alternating operations.

In this series: \[ 7,\;10,\;16,\;28,\;52 \] Differences follow: \[ 3,\;6,\;12,\;24,\;48 \] So the next term is: \[ 52 + 48 = 100 \]

Answer 1

The Correct Option is D

Concept:
In number series questions, we often identify patterns in the differences between consecutive numbers. Many series follow patterns such as increasing differences, multiplication patterns, or combinations of arithmetic operations. A useful strategy is to calculate the difference between consecutive terms to detect a pattern.
Step 1: Write the given series.
\[ 7,\; 10,\; 16,\; 28,\; 52,\; ? \]
Step 2: Find the differences between consecutive numbers.
\[ 10 - 7 = 3 \] \[ 16 - 10 = 6 \] \[ 28 - 16 = 12 \] \[ 52 - 28 = 24 \] Thus, the differences are: \[ 3,\; 6,\; 12,\; 24 \]
Step 3: Identify the pattern in the differences.
Each difference is double the previous one: \[ 3 \times 2 = 6 \] \[ 6 \times 2 = 12 \] \[ 12 \times 2 = 24 \] Therefore, the next difference should be: \[ 24 \times 2 = 48 \]
Step 4: Find the next term in the series.
\[ 52 + 48 = 100 \] Thus, the next number in the series is: \[ 100 \]
Step 5: Selecting the correct option.
\[ \boxed{100} \] Hence, the correct answer is: \[ \text{Option (C) } 100 \]