SQL Server database backup to store only the last 7 backups in a file
I would recommend you to study and implement  Ola Hallengren's SQL Server Backup solution. Its free and is widely tested and recognized in the community.

e.g :

Back up all user databases, using checksums and compression; verify the backup; and delete old backup files

EXECUTE dbo.DatabaseBackup
@Databases = 'USER_DATABASES',
@Directory = 'C:\Backup',
@BackupType = 'FULL',
@Verify = 'Y',
@Compress = 'Y',
@CheckSum = 'Y',
@CleanupTime = 24


Automate and Improve Your Database Maintenance Using Ola Hallengren's Free Script will give you a good start.