One of the most straightforward and elementary searches is the sequential search, also known as a linear search.
As a real world example, pickup the nearest phonebook and open it to the first page of names. We're looking to find the first "Smith". Look at the first name. Is it "Smith"? Probably not (it's probably a name that begins with 'A'). Now look at the next name. Is it "Smith"? Probably not. Keep looking at the next name until you find "Smith".
The above is an example of a sequential search. You started at the beginning of a sequence and went through each item one by one, in the order they existed in the list, until you found the item you were looking for. Of course, this probably isn't how you normally look up a name in the phonebook; we'll cover a method similar to the way you probably look up phone numbers later in this guide.
Now we'll look at this as related to computer science. Instead of a phonebook, we have an array. Although the array can hold data elements of any type, for the simplicity of an example we'll just use an array of integers, like the following: