Explanation:

Now in the given series 3, 14, 29, 38, 51, 58, 69, ? we can note two things which are:

The numbers are in ascending order which means that the numbers are increasing along the series rather than decreasing.The series is systematic and progressive.

Second thing is that in the given numbers the progressing number is a result of adding an odd number to the previous one.For example,

3+11=14

14+15=29 and so on.

Now in the given options the first two options are clearly not valid as they are smaller than the last number given in the series which is 69.

now keeping the second condition in mind which adding an odd number to the series we get 74 as the correct answer.

69+5=74