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.
Learn more about Math Pattern