Many third party scripts provide built-in captcha functionality. However due to some mis-configuration, it may not be displayed on your website. Following are some reasons for captcha not being displayed:
 Captcha is using image libraries like GD, ImageMagick etc. Make sure that you meet the necessary requirements and enable necessary binaries. If they are not enabled, you can contact your web hosting provider.
 Sometime some encode files/images are corrupted during upload. It is recommended to select “Auto Detect” option in your FTP client during upload.
 If your Captcha is using API, there may be a connection problem between your website’s server and API server.
There may be some other reasons as well for this problem.