Discussion
Find the next term.
0.5, 0.6, 1.5, 4, 8.9, ______
Answer: D
The successive differences of 0.5, 0.6, 1.5, 4, 8.9 are 0.1, 0.9, 2.5, 4.9, which are \(0.1\times1^{2}\), \(0.1\times3^{2}\), \(0.1\times5^{2}\) and \(0.1\times7^{2}\), the squares of the odd numbers.
The next difference is \(0.1\times9^{2}=8.1\), so the next term is 8.9 + 8.1 = 17.0, option D. The values 12.6, 13.5 and 14.3 do not follow the pattern.
A series whose differences are squares of odd numbers scaled by 0.1 is a typical aptitude pattern, and the check 0.5 + 0.1 = 0.6, 0.6 + 0.9 = 1.5, 1.5 + 2.5 = 4.0, 4.0 + 4.9 = 8.9 confirms it.
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