Question

Look at this series: $7,\; 10,\; 8,\; 11,\; 9,\; 12,\; \ldots$ What number should come next?

• A. 7
• B. 10
• C. 12
• D. 13

Hint:

For mixed-up series, try (i) looking at alternating $+\!/-$ patterns, and (ii) splitting into two subsequences (odd/even positions). If both agree, you’ve cracked it.

Answer 1

The Correct Option is B

Method A — Alternating differences Step A1 (Compute successive changes).
$7 \to 10 : +3$;\; $10 \to 8 : -2$;\; $8 \to 11 : +3$;\; $11 \to 9 : -2$;\; $9 \to 12 : +3$.
Pattern: $+3,\; -2,\; +3,\; -2,\; +3,\; \ldots$ Step A2 (Apply the next change).
After $+3$ at $9 \to 12$, the next change should be $-2$.
Thus, next term $= 12 - 2 = 10$. Method B — Two interleaving subsequences (confirmation) Step B1 (Separate odd/even positions).
Odd positions: $7, 8, 9, \ldots$ (increase by $+1$).
Even positions: $10, 11, 12, \ldots$ (increase by $+1$). Step B2 (Identify which position comes next).
Given six terms, the next is position $7$ (odd). The odd-position subsequence continues $7,8,9,\boxed{10},\ldots$ Step B3 (Consistency check).
Both methods yield the same next term $$ answer is reliable. \[ \boxed{10\ \text{(Option (b)}} \]