The given sentence states past actions 'a week ago' and 'yesterday'.
Hence, the sentence is in simple past tense.
Also, the first part is in passive voice, because the subject 'the letter' experiences the action 'to be posted'. It cannot perform the action 'to post'.
The second part 'to arrive' is in active voice, as it can perform the action 'to arrive'.
Option B: 'Was posted' is in simple past tense, passive voice.
'Arrived' is in simple past tense, active voice.
It agrees to the situation presented. Hence option B is correct.
Option A: 'Is posted' and 'is arrived' are in simple present tense and do not agree with the past situation.
Option C: 'Posted' is in active voice, as opposed to the first part of the sentence in passive voice.
Option D: 'Posts' and 'arrives' refer to present actions, whereas the sentence happened in the past.
Hence options A, C and D are incorrect.