Which number will replace the question mark (?) in the following series? $3, 8, 6, 11, 9, 14, 12, ?$
Explanation:
The given series is $3, 8, 6, 11, 9, 14, 12, ?$. This is an alternating series, which can be broken down into two separate sub-series: Sub-series 1 (terms at odd positions): $3, 6, 9, 12, \dots$. Analyzing this: $3 \xrightarrow{+3} 6 \xrightarrow{+3} 9 \xrightarrow{+3} 12$. This is an arithmetic progression with a common difference of $+3$. Sub-series 2 (terms at even positions): $8, 11, 14, ?, \dots$. Analyzing this: $8 \xrightarrow{+3} 11 \xrightarrow{+3} 14$. This is also an arithmetic progression with a common difference of $+3$. The next term in the original series is the next term in Sub-series 2. So, the next term in Sub-series 2 will be $14 + 3 = 17$. Let's analyze the options: A) $18$: Implies $14+4$, inconsistent. B) $15$: Implies $14+1$, inconsistent. C) $16$: Implies $14+2$, inconsistent. D) $17$: This option perfectly matches the derived pattern of adding $3$ to the previous term in the second sub-series.