Question

Find the missing term in the following series: 1, 3, 4, 9, ___, 27, 10

• A. 7
• B. 12
• C. 11
• D. 13

Hint:

Separate alternating terms in such series. Often one sequence is arithmetic and the other geometric.

Answer 1

The Correct Option is A

Let’s split the series into two alternate sequences: Odd positions: 1, 4, \_\_, 10
Even positions: 3, 9, 27 Even positions pattern: \[ 3 \times 3 = 9,\quad 9 \times 3 = 27 \Rightarrow \text{Multiplying by 3} \] Odd positions pattern: \[ 1 \rightarrow 4 \ (\text{+3}) \\ 4 \rightarrow ? \ (\text{+3}) \Rightarrow 4 + 3 = 7 \\ 7 \rightarrow 10 \ (\text{+3}) \] So, the missing term is: \[ \boxed{7} \]