The tenth term in the following sequence: 1, 5, 14, 30, 55, ……….

Correct option is D

Now, let's find the differences between consecutive terms:

• 5 - 1 = 4
• 14 - 5 = 9
• 30 - 14 = 16
• 55 - 30 = 25

We can see that the differences (4, 9, 16, 25) are perfect squares:

• 2² = 4
• 3² = 9
• 4² = 16
• 5² = 25

The differences are the squares of consecutive integers (2, 3, 4, 5). If this pattern continues, the next difference should be:

• 6² = 36

Thus, to find the 6th term, we add 36 to 55:

• 55 + 36 = 91

Next, the difference will be 7² = 49 for the 7th term:

• 91 + 49 = 140

Then, the difference for the 8th term is 8² = 64:

• 140 + 64 = 204

For the 9th term, the difference will be 9² = 81:

• 204 + 81 = 285

Finally, the difference for the 10th term is 10² = 100:

• 285 + 100 = 385

Thus, the 10th term in the sequence is 385.