Discussion
In the series 3, 10, 24, 50, ..., what will be the 7th term?
Answer: C
The 7th term is 288.
The terms come from the prime numbers 2, 3, 5, 7, ... squared, alternately minus and plus 1:
\[ \begin{aligned} 2^{2} - 1 &= 3,\quad 3^{2} + 1 = 10 \\ 5^{2} - 1 &= 24,\quad 7^{2} + 1 = 50 \end{aligned} \]
Continuing, \(11^{2} - 1 = 120\), \(13^{2} + 1 = 170\), and the 7th term uses the 7th prime, 17: \(17^{2} - 1 = 288\). 290 is \(17^{2} + 1\), with the sign pattern broken, and 224 and 226 do not fit.
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