When writing an application letter, you should make sure it is targeted for the specific program or position.
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In an application letter you shouldn’t tell how you heard about the program you are applying for.
Upon receiving an invitation, no matter whether you accept it or not, it is polite of you to reply promptly.
When responding to a letter of invitation, you can start by mentioning the main contents of the invitation briefly.
If you invite somebody to speak at a conference, you should mention in the invitation letter the type of speech, the topic or the scope and how long the speech will be.