I utilized below mentioned code in a class and used that class in a trigger to update a field at Account Level but it's giving me Trigger Recursion Error.( I know this can be done via simple workflow but want to understand how this can be achieved via apex)

(This code is from Apex Developers Guide. Here is the link:
https://developer.salesforce.com/docs/atlas.en-us.apexcode.meta/apexcode/langCon_apex_dml_examples_insert_update.htm)

Account[] accts = new List<Account>();
for(Integer i=0;i<3;i++) {
Account a = new Account(Name='Acme' + i,
BillingCity='San Francisco');
accts.add(a);
}
Account accountToUpdate;
try {
insert accts;
// Update account Acme2.
accountToUpdate =
[SELECT BillingCity FROM Account
WHERE Name='Acme2' AND BillingCity='San Francisco'
LIMIT 1];
// Update the billing city.
accountToUpdate.BillingCity = 'New York';
// Make the update call.
update accountToUpdate;
} catch(DmlException e) {
System.debug('An unexpected error has occurred: ' + e.getMessage());
}
 
// Verify that the billing city was updated to New York.
Account afterUpdate =
[SELECT BillingCity FROM Account WHERE Id=:accountToUpdate.Id];
System.assertEquals('New York', afterUpdate.BillingCity);

I utilized below mentioned code in a class and used that class in a trigger to update a field at Account Level but it's giving me Trigger Recursion Error.( I know this can be done via simple workflow but want to understand how this can be achieved via apex)

(This code is from Apex Developers Guide. Here is the link:
https://developer.salesforce.com/docs/atlas.en-us.apexcode.meta/apexcode/langCon_apex_dml_examples_insert_update.htm)

Account[] accts = new List<Account>();
for(Integer i=0;i<3;i++) {
Account a = new Account(Name='Acme' + i,
BillingCity='San Francisco');
accts.add(a);
}
Account accountToUpdate;
try {
insert accts;
// Update account Acme2.
accountToUpdate =
[SELECT BillingCity FROM Account
WHERE Name='Acme2' AND BillingCity='San Francisco'
LIMIT 1];
// Update the billing city.
accountToUpdate.BillingCity = 'New York';
// Make the update call.
update accountToUpdate;
} catch(DmlException e) {
System.debug('An unexpected error has occurred: ' + e.getMessage());
}
 
// Verify that the billing city was updated to New York.
Account afterUpdate =
[SELECT BillingCity FROM Account WHERE Id=:accountToUpdate.Id];
System.assertEquals('New York', afterUpdate.BillingCity);