What is the recursive formula for this arithmetic sequence -16,-7,2,11,

Hello from MrBillDoesMath!

a(n) = -16                    when n = 1

a(n) = a(n-1) + 9          when  n > 1 ( i.e. n = 2,3,4)

Discussion:

First observation:

-16 + 9 = -7

-7  + 9 = 2

2   + 9 = 11

So the pattern seems to be gotten by addition of 9 to each number. The recursive formula therefore is this:

a(n) = -16                    when n = 1

a(n) = a(n-1) + 9         where  n > 1 ( i.e. = 2,3,4)

Thank you,

MrB

options a,b,c are the right answer.

step-by-step explanation:

a linear parent function is always represented as y = x

if we write this function in the form of y=mx+c

⇒

or  

now if we plot a graph we will find these characteristics:

1) y intercept of the graph is zero so its a straight line passing through origin.

2) as we can see in both the forms of function written, values of x and y may be either positive or negative for the positive slope means points on the graph are either in first quadrant or in third one.

3) it's slope is one.