0.5, 2, 4.5, 8, 12.5, 18, 24.5,....
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31
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32
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31.5
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32.5
The sequence follows the pattern n(n+1)/2: 0.5(1×1/2), 2(2×2/2), 4.5(3×3/2), 8(4×4/2), 12.5(5×5/2), 18(6×6/2), 24.5(7×7/2). The next term is 8×8/2 = 32. The differences between terms increase by 1.5, 2.5, 3.5, 4.5, 5.5, 6.5, so the next difference is 7.5, making 24.5+7.5=32.
To find the pattern in the given sequence, let's look at the differences between consecutive terms:
1st difference: 2 - 0.5 = 1.5 2nd difference: 4.5 - 2 = 2.5 3rd difference: 8 - 4.5 = 3.5 4th difference: 12.5 - 8 = 4.5
We can observe that the differences are increasing by 1 each time. Therefore, the next difference should be 5.5.
To find the next term in the sequence, we add the next difference to the last term in the sequence:
24.5 + 5.5 = 30
Hence, the next term in the sequence should be 30.
Now, let's go through each option to see which one matches the pattern:
A. 31 - This option is incorrect because it does not match the pattern. B. 32 - This option is correct because it matches the pattern. C. 31.5 - This option is incorrect because it does not match the pattern. D. 32.5 - This option is incorrect because it does not match the pattern.
Therefore, the correct answer is B) 32.