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The pattern below is made of pennies.

1st Term: No pennies


2nd Term: 3 pennies


3rd Term: 8 pennies


4th term: 15 pennies



Describe a rule you could use to find the number of pennies needed to make any term in the pattern.

User Boky
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1 Answer

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Final answer:

The number of pennies needed for any term can be calculated using the formula n^2 - 1, where 'n' represents the term number.

Step-by-step explanation:

Looking carefully at the pattern, we can notice that the number of pennies required for any term is actually one less than the term number squared, or n^2 - 1, where 'n' denotes the term number. For example, for the 2nd term, 2^2 equals 4. Subtracting 1 yields 3, which is indeed the number of pennies required for the 2nd term. Similarly, for the 3rd term, 3^2 is 9, and 9 minus 1 gives us 8 pennies. Hence, for any term n, the number of pennies needed is n^2 minus 1.

The pattern you've described appears to be related to the arrangement of pennies in a triangular pattern, where each term represents the number of pennies needed to form a triangle with increasing rows. To find a rule to determine the number of pennies needed for any term in the pattern, you can observe that the pattern is following a quadratic sequence.

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User Schiza
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