Find the next term of the following number series : 1, 4, 10, 22, 46 ......

Question

Accepted Answer

To determine the next term in the series 1, 4, 10, 22, 46, we need to identify the pattern or rule governing the sequence. Let's analyze the differences between consecutive terms:

1. The difference between the first term (1) and the second term (4) is 3.
2. The difference between the second term (4) and the third term (10) is 6.
3. The difference between the third term (10) and the fourth term (22) is 12.
4. The difference between the fourth term (22) and the fifth term (46) is 24.

Observing these differences, we notice a pattern: each difference is double the previous difference.

- 3 (3 x 1)
- 6 (3 x 2)
- 12 (3 x 4)
- 24 (3 x 8)

The pattern suggests that the differences are increasing by a factor of 2 each time. Therefore, the next difference should be 24 x 2 = 48.

Adding this difference to the last term in the series:

46 + 48 = 94

Thus, the next term in the series is 94, which corresponds to Option 3.

Now, let's explain why the other options are incorrect:

1. Option 1 (70): If we add 24 (the last difference) to 46, we get 70. However, this does not follow the pattern of doubling the previous difference.

2. Option 2 (86): This option does not fit the pattern of doubling the previous difference. The correct difference should be 48, not 40.

4. Option 4 (122): This option exceeds the expected next term based on the pattern of differences. The correct difference should be 48, not 76.

Therefore, based on the pattern of differences, Option 3 (94) is the correct answer.