The first paragraph states the reason(s) for writing and, if needed, what you are responding to (an advert, a prospectus...).
In addition, an opening paragraph is needed to make reference to previous correspondence.
EXAMPLE: I would like to apply for one of the scholarships I saw advertised in your prospectus. (applying for a scholarship)
EXAMPLE: I am the secretary of my college ... I am interested in organising a group visit ... I was wondering if I could ask some questions about it. (requesting information)
EXAMPLE: I am writing (in order) to complain about the ... (complaint letter)
EXAMPLE: I am writing with regard to ... I am writing with reference to... I am writing in response to...
EXAMPLE: Thank you for / your letter of 9 May... / for your letter regarding...
EXAMPLE: In reply to your letter of 8 May, ...
Learning English 'FCE Formal Letter' Retrieved from http://www.rubenvalero.com/english/content/fce-formal-letter-or-email
Oxford Living Dictionaries 'Choose the right greeting and sign off'. Retrieved from https://en.oxforddictionaries.com/writing-help/choose-the-right-greeting-and-sign-off
Oxford University Press 'Sample formal letter' ["PDF file] Retrieved from https://oup.useremarkable.com/production/images/uploads/3687/original/uk_sample_formal-letter.pdf