What is the recursive formula for this arithmetric sequence?

Question

-16, -7, 2, 11

A. {a₁= -16

{a_n = a_n-1 +9

B. {a₁= 11

{a_n = a_n-1 -9

C. {a₁= 11

{a_n = a_n-1 +9

D. { a₁= 16

{a_n = a_n-1 -9

Answer 1

Lets make a little table for the sequence you listed:

So since -16 is the first term it is a₁ and since 11 is the 4th term, it is a₄.

Now, let's look at the answers:

A. If n = 2, then the equation says a₂ = a₁ + 9 and since a₁ is -16 and a₂ is -7, it says -7 = -16 + 9 and that is a true statement.so this looks like the correct answer. But let's try the others:

B. This answer is backwards. It calls the last term as the first term, etc.

C. This answer again starts at the end but then keeps going beyond the sequence of numbers.

D. This starts with 16 which isn't even in the sequence.

So the answer is A