Language/English/Grammar/Alternate(ly)-and-alternative(ly)

Alternate(ly) and alternative(ly) 

Alternate(ly) means ‘first one and then the other’, 'in turns'. 

Examples:

We spend alternate weekends at our country cottage.

I ’m alternately happy and depressed. 

Alternatively is similar to 'different', ‘instead’, 'on the other hand. 

Examples:

Jessica’s not free on the 29th. We’ll have to find an alternative date.

You could go by air, or alternatively you could drive there.  

*In American English alternately can be used with the same meaning as alternatively.