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Answer:

nth term: 0.5n² + 2.5n + 3

Explanation:

pattern 1 = 6 bowls

pattern 2 = 10 bowls

pattern 3 = 15 bowls

pattern 4 = 21 bowls

First difference:

  • 10 - 6 = 4
  • 15 - 10 = 5
  • 21 - 15 = 6

Second difference:

  • 5 - 4 = 1
  • 6 - 5 = 1

This is not an arithmetic nor a geometric sequence.

Solve:

2a  = 2nd difference

2a = 1

a = 1/2 or 0.5

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3a + b = 1st difference

3a + b = 4

b = 4 - 3(1/2)

b = 2.5

====================

a + b + c = first term

1/2 + 2.5 + c = 6

c = 3

Quadratic nth term:

0.5n² + 2.5n + 3

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