It is clear that a large survey is an appropriate method for a study of marriage patterns among college students. What will the researcher need to do to insure that the research sample is random?

Here the sample is the college students, and the researcher want's to do a survey to obtain information about marriage patterns.

Then, the ideal sample will be constituted of students of both genders, of different ideologies, of different social classes, of different religions, etc.

Then the thing that the researcher needs to do is:  

Define the size of the sample

Assign to each student a unique number.

using a random number generator,  generate enough different numbers to fill the sample.

Each of these numbers corresponds to a unique student, so now you have a complete sample of random selected students.

This sample can not be biased in any way.

step-by-step :

hi there!

first we need to find out how much they are adding to each number to make the next number.

ex: 4 + 4 = 8, 8 + 8 = 16, and so on.

so continuing with 32,

32 + 32 = 64

64 + 64 = 128

128 + 128 = 256

256 + 256 = 512

4, 8, 16, 32, 64, 128, 256, 512

the 8th term of the sequence will be 512

hope this ! ~