Discussion
The sum of next two numbers in the pattern 3, 10, 32, 99, _____, _____ is
Answer: C
The sum of the next two numbers is 1209.
Each term is three times the previous term plus a number that goes up by 1 each time:
\[ \begin{aligned} 3 \times 3 + 1 &= 10 \\ 10 \times 3 + 2 &= 32 \\ 32 \times 3 + 3 &= 99 \\ 99 \times 3 + 4 &= 301 \\ 301 \times 3 + 5 &= 908 \end{aligned} \]
So the next two numbers are 301 and 908, and \(301 + 908 = 1209\).
Spotting only the 'multiply by 3' part and missing the growing addition is the usual trap; the next terms must keep the rule, so 302 or 300 in place of 301 would break it.
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