Question

Which is the recursive formula for this arithmetic sequence?

an = an – 1 + 7 where a1 = –10

an = an – 1 + 17 where a1 = –10

an = 7an – 1 - 17 where a1 = –10

an = an – 1 – 7 where a1 = –10

Answer 1

an = a_{n-1} + 7, where a1 = −10.

Reason: an arithmetic sequence has constant difference d. Here the terms increase by 7 each step, so the recursive rule is a_n = a_{n-1} + 7. (The option 7·a_{n-1} − 17 is not arithmetic.)