In order to close your Blogger account, you need to delete your Google account. However, all other accounts that associate to your Google account (such as Gmail, Youtube, etc.) will be deleted too. See this page for more info: https://support.google.com/accounts/answer/32046
Finally, if you just want to delete your blog, please follow the instructions on this page: https://support.google.com/blogger/answer/41387?hl=en