Q5 - Problem solving

The correct answer is E) 12.

The pattern is that each number equals twice the previous number plus the number before that. Starting with 1 and 2:

You find it by trying simple relationships between nearby numbers.

First, check whether you’re adding the same amount each time: 1 → 2 is +1, but 2 → 5 is +3, so that doesn’t work. Multiplying by a fixed number doesn’t work either.

Next, look at the terms that are already known at the end: 29, 70, 169. Notice that 70 is a little more than twice 29:

70 − (2 × 29) = 12

Now check the next step:

169 − (2 × 70) = 29

That remainder, 29, is the number two places before 169. This suggests the rule: double the previous number, then add the number before it.

Check it at the beginning:

• 2 × 2 + 1 = 5

• 2 × 5 + 2 = 12

• 2 × 12 + 5 = 29

Everything fits, so x = 12. The trick is to try a simple rule, then check that it works throughout the sequence.