Find the next term of the following
number series :
4, 10, 23, 50, 105, ?

Question

Find the next term of the following
 number series :
 4, 10, 23, 50, 105, ?

Accepted Answer

To determine the next term in the series 4, 10, 23, 50, 105, we need to identify the pattern or rule governing the sequence. Let's analyze the differences between consecutive terms:

1. Difference between 10 and 4: 10 - 4 = 6
2. Difference between 23 and 10: 23 - 10 = 13
3. Difference between 50 and 23: 50 - 23 = 27
4. Difference between 105 and 50: 105 - 50 = 55

Observing these differences, we notice a pattern:

- The differences themselves are increasing in a specific manner: 6, 13, 27, 55.

Let's examine the differences between these differences:

1. Difference between 13 and 6: 13 - 6 = 7
2. Difference between 27 and 13: 27 - 13 = 14
3. Difference between 55 and 27: 55 - 27 = 28

The differences between the differences are: 7, 14, 28. This sequence is doubling each time (7 x 2 = 14, 14 x 2 = 28).

Following this pattern, the next difference should be 28 x 2 = 56.

Adding this to the last difference in the original series:

55 + 56 = 111

Now, add this difference to the last term in the series:

105 + 111 = 216

Therefore, the next term in the series is 216, which corresponds to Option 2.

Explanation for why other options are incorrect:

1. Option 1 (215): This option is incorrect because it does not follow the established pattern of differences and their subsequent increases.
2. Option 3 (218): This option is incorrect because it does not align with the calculated next term based on the pattern of differences.
3. Option 4 (220): This option is incorrect because it does not fit the logical progression of the series as determined by the pattern of differences.

Thus, Option 2 (216) is the correct answer, as it accurately follows the pattern identified in the series.