_{_{a_1=12,\ a_{n+1}=a_n-3}}

Question

i am clueless

Answer 1

This is a sequence. This sequence is called "a" and it is made up of terms. Each term has a subscript name, "a₁" is the first term, "a₂" is the second term, and so forth. We can generically denote terms as "a_n" where we can specify "n" to get a specific term (if n = 3, then we mean the third term "a₃"). If "a_n" is the term we are speaking about, then the term after that would be "a_n+1" because "n" is one bigger than the term we are speaking about.

In this case, the equation a_n+1 = a_n - 3 tells us how to get the next term if we know the term we are on. It says, take the term you are on (which is a_n) and subtract 3 to get to the next term (a_n+1). Since we are told that the first term (a₁) is 12, then the second term is 12 - 3 or, in other words 9. If the second term is 9, then the third term is 6 (9 - 3 = 6), and the fourth term is 3.

So this sequence can be written as: 12, 9, 6, 3, 0, -3, -6, -9, -12, -15, . . .