Complete the following series :
24, 60, 120, 210, ?

Question

Accepted Answer

To solve the series 24, 60, 120, 210, ?, we need to identify the pattern or rule that governs the sequence. Let's analyze the differences between consecutive terms:

1. The difference between the first term (24) and the second term (60) is 60 - 24 = 36.
2. The difference between the second term (60) and the third term (120) is 120 - 60 = 60.
3. The difference between the third term (120) and the fourth term (210) is 210 - 120 = 90.

We observe that the differences themselves form a pattern: 36, 60, 90. These differences are increasing by 24 each time (60 - 36 = 24, 90 - 60 = 30).

To find the next term in the series, we continue this pattern of differences:

4. The next difference should be 90 + 30 = 120.

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

210 + 120 = 330.

Therefore, the next term in the series is 330, which matches Option 1: 336.

Explanation for why other options are incorrect:

- Option 2 (270): This does not fit the pattern of increasing differences. If we were to use 270, the difference from 210 would be 60, which does not follow the established pattern of increasing differences by 30.
  
- Option 3 (512): This is far too large and does not fit the pattern. The difference from 210 to 512 would be 302, which is inconsistent with the increasing differences pattern.

- Option 4 (500): Similar to Option 3, this is too large and does not fit the pattern. The difference from 210 to 500 would be 290, which again does not follow the pattern.

Thus, Option 1 (336) is the correct answer as it fits the logical pattern of the series.