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"Seguir" is a transitive verb which is often translated as "to follow", and "perseguir" is a transitive verb which is often translated as "to pursue". Learn more about the difference between "seguir" and "perseguir" below.
seguir(
seh
-
geer
)A transitive verb is a verb that requires a direct object (e.g., I bought a book.).
a. to follow 
Sígueme y te enseño el camino a casa.Follow me and I will show you the way home.
Los niños siguieron a su padre hasta el parque.The children followed their dad to the park.
4. (to study)
a. to follow 
Millones de adolescentes siguen al cantante en Twitter.Millions of teenagers follow the singer on Twitter.
An intransitive verb is one that does not require a direct object (e.g., The man sneezed.).
6. (to resume)
a. to carry on 
¿Seguimos o prefieres tomar un descanso?Shall we carry on or would you rather have a break?
b. to go on 
No podemos seguir así. Hay que hacer algo.We can't go on like this. We have to do something.
c.  no direct translation
This refers to an idiomatic word or phrase for which there is no word-for-word translation.
¿Tu hermana sigue acusándote de haberle robado la pulsera?Is your sister still accusing you of stealing her bracelet?
Seguimos bailando hasta no poder más.We kept dancing until we couldn't go on anymore.
a. to carry on 
Sigan por el malecón unos cinco minutos y verán el restaurante a la derecha.Carry on along the boardwalk for five minutes and you'll see the restaurant on your right.
b. to keep going 
Siga todo recto hasta el banco y luego doble a la izquierda.Keep going straight ahead as far as the bank and then turn left.
11. (to persist)
a.  no direct translation
This refers to an idiomatic word or phrase for which there is no word-for-word translation.
Seguimos sin saber si van a venir a la boda o no.We still don't know if they're coming to the wedding or not.
Mejor que aplacemos la salida porque sigue nevando.We'd better delay our departure because it is still snowing.
seguirse
A pronominal verb always uses a reflexive pronoun. (e.g., Te ves cansado.).
12. (to deduce)
a. to follow 
Por tus malas notas se sigue que no has estudiado en absoluto.From your bad grades, it follows that you have not studied at all.
a. to follow 
Las etiquetas HTML en esta secuencia deben seguirse una tras otra sin un espacio intermedio.The HTML tags in this sequence need to follow one after the other without an intervening space.
perseguir(
pehr
-
seh
-
geer
)A transitive verb is a verb that requires a direct object (e.g., I bought a book.).
a. to pursue 
La policía persiguió al criminal por tres días antes de capturarlo.The police pursued the criminal for three days before capturing him.
b. to follow 
El agente persiguió al vehículo sospechoso por seis cuadras.The agent followed the suspicious vehicle for six blocks.
c. to chase 
El león perseguirá la gacela hasta que se canse.The lion will chase the gazelle until it gets tired.
a. to pursue 
Ella siempre ha perseguido una carrera como actriz.She has always pursued a career as an actress.
3. (to pester)
a. to harass 
Suele perseguir a la gente hasta que consigue lo que quiere.He tends to harass people until he gets what he wants.
4. (to oppress)
a. to persecute 
Durante la inquisición del siglo XVI, se persiguió fuertemente a los judíos.During the inquisition of the 16th century, Jews were heavily persecuted.