Question

A series is given with two terms missing. Choose the correct alternatives from the given ones that will complete the series:
3, 5, 35, 10, 12, 35, ___, ___}

• A. 19, 35
• B. 17, 19
• C. 19, 24
• D. 22, 35

Hint:

Try grouping terms (pairs or triplets) when a pattern is not obvious in a straight sequence.

Answer 1

The Correct Option is A

Concept: Observe the pattern in groups of three. Step 1:Group the series: \[ (3, 5, 35), \quad (10, 12, 35), \quad (__, __) \]
Step 2:Identify pattern in each group: \[ 3 \times 5 + 20 = 35 \] \[ 10 \times 12 + (-85) \text{ (not consistent)} \] Instead, observe another pattern: First two numbers increase by: \[ 3 \rightarrow 10 \rightarrow 19 \quad (+7, +9) \] \[ 5 \rightarrow 12 \rightarrow ? \quad (+7, +7) \] So: \[ 12 + 7 = 19 \]
Step 3:Notice repetition: \[ 35 \text{ appears after every pair} \]
Step 4:Complete the series: \[ 3, 5, 35, 10, 12, 35, 19, 35 \]
Step 5:Final Answer: \[ (19, 35) \]