Question

A cereal company adds baseball cards to the 3rd box, the 6th box, the 11th box the 18th box, and so on of each case of cereal. In a case of 40 boxes, how many boxes will have baseball cards?

Explain how you got your answer.

Answer 1

Answer: 6 boxes

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Step-by-step explanation:

The sequence 3, 6, 11, 18 has gaps of 3, 5, 7

Subtract the adjacent values to find the gaps.

• 6-3 = 3
• 11-6 = 5
• 18-11 = 7

If this pattern continues, then we'd have this extended sequence

3, 6, 11, 18, 27, 38, 51

We stop once we reach 40 or get over it

Notice that

• 18+9 = 27
• 27+11 = 38
• 38+13 = 51

The sequence {3,6,11,18,27,38} has 6 values listed. So 6 boxes will get a baseball card.