A sequence has its first term equal to 8, and each term of the sequence is obtained by adding 6 to the previous term. If f(n) represents the nth term of the sequence, which of the following recursive functions best defines this sequence?
A recursive formula for an arithmetic sequence is: a(n)=a(n-1)+d, where n=term number and d=common difference. Since we are told that d=6: a(n)=a(n-1)+6, a1=8 They may want: f(n)=f(n-1)+6, a1=8 I never understood why they teach this instead of explicit formulas because the above is pretty useless if you simply want say the 1031st term, you would need to do a lot of calculations to find it. :P. The explicit function is: a(n)=a+d(n-1), here a=8 and d=6 so a(n)=8+6(n-1) a(1031)=8+6(1031-1)=6188 Try finding the 1031st term with the recursive formula :D