3, 8,18,38,80,158,318a)18b)158 c)3d)318e)80Correct answer is option 'E'. Can you explain this answer?

Question

3, 8,18,38,80,158,318a)18b)158        c)3d)318e)80Correct answer is option 'E'. Can you explain this answer?

Answer

The solution is:
3 * 2 + 2 = 8
8 * 2 + 2 = 18
18 * 2 + 2 = 38
38 * 2 + 2 = 78 ≠ 80
78 * 2 + 2 = 158
158 * 2 + 2 = 318
Therefore, wrong no. is 80

Answer

Answer

To find the pattern in the given sequence 3, 8, 18, 38, 80, 158, 318, let's analyze the differences between consecutive terms:

1. First Difference:
The difference between 8 and 3 is 5.
The difference between 18 and 8 is 10.
The difference between 38 and 18 is 20.
The difference between 80 and 38 is 42.
The difference between 158 and 80 is 78.
The difference between 318 and 158 is 160.

2. Second Difference:
The difference between 10 and 5 is 5.
The difference between 20 and 10 is 10.
The difference between 42 and 20 is 22.
The difference between 78 and 42 is 36.
The difference between 160 and 78 is 82.

From the above analysis, we can observe that the second differences are not constant. Therefore, the given sequence does not follow a linear pattern.

Next, let's analyze the first differences to see if there is any pattern:

3. First Differences:
The first differences are 5, 10, 20, 42, 78, 160.

From the first differences, we can observe that each term is increasing by a multiple of 2:

5 * 2 = 10
10 * 2 = 20
20 * 2 = 40
40 * 2 = 80
80 * 2 = 160

Therefore, we can conclude that the first differences follow a pattern of multiplying the previous term by 2.

Now, let's apply this pattern to the last term of the given sequence:

318 * 2 = 636

Therefore, the next term in the sequence would be 636.

Finally, let's verify which option matches this answer:

a) 18: Incorrect
b) 158: Incorrect
c) 3: Incorrect
d) 318: Incorrect
e) 80: Incorrect

None of the given options match our answer, so there might be an error in the options provided. However, based on the pattern analysis, the next term in the sequence should be 636.

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