Discussion
Select the number that will come next in the following series.
114, 127, 153, 192, 244, __________.
Answer: C
The next number is 309.
Look at the differences between terms:
\[ \begin{aligned} 127 - 114 &= 13,\ 153 - 127 = 26 \\ 192 - 153 &= 39,\ 244 - 192 = 52 \end{aligned} \]
The differences are 13, 26, 39, 52, the multiples of 13, so the next difference is 65 and the next term is \(244 + 65 = 309\). 284 adds only 40, while 344 and 352 add 100 and 108, breaking the pattern of multiples of 13.
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