“We've been going through a period of weak sales.”

Your company's sales numbers have been decreasing for 3 months. You are giving a presentation to some coworkers and say this to point out the problem.

We've been going through a period of weak sales.

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go through (something)

People use the phrase "go through ___" to describe negative experiences. "Go through" means to experience something negative or difficult. Some examples include:

go through a divorce

go through a tough time

go through a period of weak sales

go through childbirth

There are some other totally different meanings of "go through". One is to search and examine things in a list or a collection:

We should sit down and go through the details later this week.

Another meaning of "go through" is to use a person or agency to do something for you instead of doing it directly yourself:

Are you going through a recruitment agency?

It's best to remember each of these meanings separately.

(someone) has been (doing something) for (a length of time)

"___ has been ___ing" is used to show an action or a situation that has continued for some length of time, and is still happening now:

We've been saving up for a trip to Paris.

Have you been working out?

The length of time that the action has continued is expressed with "for ___".

a period of (something)

You can use "period" to describe a specific length of time that has certain characteristics. In the example above, the period is identified as one of "weak sales". Periods can last anywhere from several days to many years.

A few more common examples used with "period" are:

a growth period

a period of transition

a period of war

a period of depression

an artistic period (in a person's life)

weak sales / strong sales

"Sales" are the number of items you sell or the amount of money you make from selling things. Sales can be either "weak" (not much) or "strong" (a lot).

the last (number)(minutes/hours/days/weeks/etc.)

This phrase tells how long something happened up until now. In positive sentences, it means that something continued from the time specified until now:

I was in Boston for the last 3 days.

In negative sentences, it means that something did not happen during that time:

We haven't eaten anything for the last 8 hours.

You can say a specific number, or use a general word like "few" or "several":

She hasn't heard from him in the last several days.