What is the next number of the following sequence? 7, 14, 55, 110, ....?

This is a digit-reversal series: each term is generated by adding the previous term to the number obtained by reversing its own digits (the reverse-and-add rule). Unlike an arithmetic or geometric progression, the increment itself changes at every step because it depends on the previous term's own digits.

1. Start with 7. The reverse of 7 is 7. So 7 + 7 = 14.

2. Take 14. The reverse of 14 is 41. So 14 + 41 = 55.

3. Take 55. The reverse of 55 is 55. So 55 + 55 = 110.

4. Take 110. The reverse of 110 is 011, that is, 11. So 110 + 11 = 121.

This reverse-and-add rule correctly reproduces all three known transitions in the series (7 to 14, 14 to 55, 55 to 110), so applying the same rule once more to 110 reliably gives the next term.

Answer: 121