Final answer:
The sequence alternates between adding 6 and adding 8 to the previous number, and after calculating the pattern, the next number in the sequence that comes after 40 is found to be 48.
Step-by-step explanation:
The sequence given is 6, 12, 20, 26, 34, 40, ... To find the pattern in this sequence and thus determine the next number, we should look at the differences between consecutive terms. Doing so, we observe:
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- 12 - 6 = 6
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- 20 - 12 = 8
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- 26 - 20 = 6
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- 34 - 26 = 8
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- 40 - 34 = 6
The pattern alternates between adding 6 and adding 8 to the previous number in the sequence. Since the last difference we calculated was 6, the next difference should be 8. Therefore, adding 8 to the last number in the sequence (40) gives us 40 + 8 = 48. The next number in the sequence is 48.