1 , 3 , 6 , 8 , 16 , 18 , 36 , 38 , 76 , ?
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78
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80
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82
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142
The pattern alternates between adding 2 and doubling the previous result: 1 + 2 = 3, 3 × 2 = 6, 6 + 2 = 8, 8 × 2 = 16, 16 + 2 = 18, 18 × 2 = 36, 36 + 2 = 38, 38 × 2 = 76. The next step is 76 + 2 = 78.
To find the pattern in the given sequence, let's look at the differences between consecutive terms:
1, 3, 6, 8, 16, 18, 36, 38, 76
The differences are:
2, 3, 2, 8, 2, 18, 2, 38
The pattern in the differences is not immediately clear. However, if we observe closely, we can see that the differences alternate between adding 2 and adding 18.
So, the next difference should be 2, which means the next term in the sequence will be obtained by adding 2 to the previous term, 76:
76 + 2 = 78
Therefore, the correct answer is A) 78.