Find the next term of the given series. $ 3, 15, 35, 63, 99, ? $
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Find the next term of the given series. $ 3, 15, 35, 63, 99, ? $
The series is n^2 - 1 for n = 2, 4, 6, 8, 10. 2^2-1=3, 4^2-1=15, 6^2-1=35, 8^2-1=63, 10^2-1=99. The next term is 12^2-1 = 144-1 = 143.
The series follows a pattern based on the difference of squares of consecutive numbers. The terms can be written as 2 squared minus 1, 4 squared minus 1, 6 squared minus 1, 8 squared minus 1, and 10 squared minus 1. Following this pattern, the next term is 12 squared minus 1, which equals 144 minus 1, or 143.