I'll have to disagree with Guest #2.
Your equations do not work if d=43 and a = 234
a(n) =a(1) + (n-1)d results in a(7) = 492 the correct answer needs to be 449
Your mistake is here: 449 =a(1) + (6-1)43 where '6' should be '7' AND at year 7 the students are at 449 SIX (not SEVEN as you described)more terms later , at year 13, the total is 750.
Soooooo the 'common difference' as you describe it is (750-449)/6 = 50 1/6 (NOT 43).
Honest mistakes we all make (frequently!)