Discussion
What is the missing number in the pattern given below ?
1, 6, 15, ____, 45, 66, 91
Answer: B
The missing number is 28.
Look at the differences between consecutive terms:
\[ \begin{aligned} 6 - 1 &= 5,\quad 15 - 6 = 9 \\ 28 - 15 &= 13,\quad 45 - 28 = 17 \\ 66 - 45 &= 21,\quad 91 - 66 = 25 \end{aligned} \]
The differences increase by 4 each time (5, 9, 13, 17, 21, 25), so the missing term is 15 + 13 = 28, and the next difference, 45 - 28 = 17, confirms it. (These are the hexagonal numbers, n(2n - 1).) 36, 32 and 25 break the pattern of differences.
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