Find the sixth term of an arithmetic sequence with t1 = 2 and tn = tn-1 + 4.

Assuming the values following t are subscripts since this is a sequence: The +4 tells that the Common difference of each term following the previous one is 4. You could keep adding by doing t2=t1 + 4 t2=2+4 = 6 t3=t3 + 4 t3=6+4 = 10 and so on. Or you could turn the recursive rule tn=t(n-1) + 4 into an explicit rule. tn = t1 + 4(n-1) So, tn = 2 + 4(n-1) where n is the term number. To the sixth term, make n=6 and solve. t(6) = 2 + 4(6-1) t(6) = 2 + 4(5) t(6) = 2 + 20 t(6) = 22 So the sixth term in this sequence is 22.

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