El ciclo de secado sigue al programa de lavado.

Because a + el contracts to al in Spanish.

So:

• a el programa → al programa

This is a mandatory contraction in normal Spanish, except when el is part of a proper name, such as a El Escorial.

In this sentence, seguir a algo means to come after / to follow something, so the verb takes a before what follows:

• sigue al programa de lavado = follows the washing programme

Sigue is the third person singular form of seguir.

Here it means:

• follows
• comes after

So:

• El ciclo de secado sigue al programa de lavado
  = The drying cycle follows the washing programme

Other common meanings of seguir include:

• to continue
• to carry on
• to follow someone or something

In this sentence, the idea is sequence: one stage comes after another.

In Spanish, de + noun is very common where English often uses a noun as an adjective.

So English:

• drying cycle
• washing programme

often becomes Spanish:

• ciclo de secado
• programa de lavado

Literally, these are like:

• cycle of drying
• programme of washing

This structure is very natural in Spanish and is often preferred over trying to make one noun directly modify another as in English.

Because here lavado is being used in a general, descriptive way: washing as a type of programme.

• programa de lavado = washing programme / wash programme

If you said del lavado, it would usually mean of the washing or from the washing, referring to a specific washing event already known in context. That is not the intended meaning here.

So:

• de lavado = general category
• del lavado = of the specific washing

Here lavado functions as a noun, meaning washing or wash.

It comes from the verb lavar (to wash), but in this sentence it is not acting as a verb. It names the type of programme:

• programa de lavado = wash programme / washing programme

The same thing happens with secado from secar:

• ciclo de secado = drying cycle

So both lavado and secado are noun-like forms here.

Spanish often uses the definite article more regularly than English does.

Here:

• El ciclo de secado = The drying cycle
• al programa de lavado = to the washing programme / after the washing programme

The first el identifies the subject: the drying cycle.

The second article is part of el programa, which becomes al programa after the contraction with a.

Even if English might sometimes say something more general like Drying follows the wash programme, Spanish usually prefers the article in a sentence like this.

Not always, because seguir has more than one use.

In this sentence, seguir a algo means to follow / come after something, so a appears:

• El secado sigue al lavado

But seguir can also mean to continue, where there may be no a:

• Sigue trabajando = He/She keeps working
• La película sigue = The film continues

So the a belongs to the meaning to follow something.

Yes, something like that can work, depending on context.

For example:

• El ciclo de secado va después del programa de lavado
• El ciclo de secado viene después del programa de lavado

These mean roughly The drying cycle comes after the washing programme.

But sigue al... is shorter and more formal/technical-sounding, which fits instructions, manuals, appliance descriptions, and similar contexts very well.

Yes, the basic structure is quite similar:

• El ciclo de secado = subject
• sigue = verb
• al programa de lavado = complement

So literally the structure is:

• The drying cycle
  • follows
    • the washing programme

This sentence uses a normal Spanish word order, and it sounds natural and neutral.

Sigue is pronounced approximately SEE-geh.

The u in gui is normally silent in Spanish unless it has a diaeresis (ü).

So:

• sigue → the u is not pronounced
• pronunciation: si-ge

The u is there to keep the g hard before e.

Compare:

• gente = soft g sound
• sigue = hard g sound

Without the u, gige would not give the right sound.

Yes. It sounds natural, especially in:

• appliance manuals
• washing machine instructions
• technical descriptions
• product interfaces or documentation

It has a slightly formal, functional tone rather than a conversational one. In everyday speech, someone might also say:

• El secado va después del lavado
• Después del programa de lavado viene el ciclo de secado

But the original sentence is perfectly normal in a technical or instructional context.