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

Step 1: Understanding the Question:
We need to identify the pattern in the given number series and find the next term.
Step 2: Key Formula or Approach:
The most common approach for number series is to find the difference between consecutive terms. If a clear pattern doesn't emerge, we can look for the difference of the differences (second-order difference) or patterns involving multiplication, squares, cubes, etc.
Step 3: Detailed Explanation:
The given series is 7, 10, 16, 28, 52, ...
Let's find the difference between consecutive terms:
\[ 10 - 7 = 3 \] \[ 16 - 10 = 6 \] \[ 28 - 16 = 12 \] \[ 52 - 28 = 24 \] The differences are 3, 6, 12, 24.
We can observe a clear pattern in these differences: each difference is double the previous one.
\[ 3 \times 2 = 6 \] \[ 6 \times 2 = 12 \] \[ 12 \times 2 = 24 \] So, the next difference in the sequence should be:
\[ 24 \times 2 = 48 \] To find the next term in the original series, we add this difference to the last term (52).
\[ \text{Next Term} = 52 + 48 = 100 \] Step 4: Final Answer:
The next number in the series is 100.