Question

7, 3, 10, 17, 27, ? — Find the missing number.

• A. 38
• B. 40
• C. 43
• D. 44 \bigskip

Hint:

For complex series, break it into parts or check secondary level of differences (e.g., difference of differences).

Answer 1

The Correct Option is D

Step 1: Analyze the series pattern.
Given: 7, 3, 10, 17, 27, ?
\[7 \to 3 \quad (-4)
3 \to 10 \quad (+7)
10 \to 17 \quad (+7)
17 \to 27 \quad (+10)\]Step 2: Continue the increment pattern.
Increment sequence: -4, +7, +7, +10, ?
Observation: Following the initial decrease, the increments are +7, +7, +10. The difference between successive increments is +3 (from +7 to +10).
Thus, the next increment might be +17 (continuing the +3 increase in increments, 7 → 10 → 17).
Alternative simpler pattern from the 3rd term:
Consider the terms 10, 17, 27. The differences are 7, 10.
The next difference could be 17 (7 + 3 = 10, 10 + 7 = 17 - this seems too large, or 10 + 3 = 13, 13 + 4 = 17). Let's re-examine the increment pattern.
Revisiting the increments: -4, +7, +7, +10.
Differences of increments: +11, 0, +3.
This is not a simple arithmetic progression.

Let's consider another perspective: the pattern of additions between terms.
7 (-4) = 3
3 (+7) = 10
10 (+7) = 17
17 (+10) = 27
Observe the additions: 7, 7, 10. The difference between these additions is: 0, 3.
This suggests the next difference in additions might be 6 (following a pattern of 0, 3, 6).
If the difference of additions is 6, then the next addition would be 10 + 6 = 16.
Therefore, the next term in the series would be 27 + 16 = 43.
Let's verify:
7, 3, 10, 17, 27, 43
-4, +7, +7, +10, +16
Differences of additions: 0, 3, 6. This looks like a coherent pattern.
\[27 + 16 = 43\]\bigskip