Find the 9th term of each arithmetic sequence

Question

-19,-13,-7,-1.... An= A1 + (n-1) d

A2 = 11.6 and A5 = 5

A5 = A2 + (5-2) d

A5 = 11.6 + 3d

d = ___

11.6 = A1 + (2-1) d

A1 = ____

An = A1 + (n-1) d

An = ______

Answer 1

Treat it like simultaneous equations:

A2=11.6 so, using the equation An = A1 + (n-1) d you get

11.6 = A1+ (2-1) d or simplified 11.6 = A1 + d

A5=5 So, 5=A1 =(5-1) d or simplified 5 = A1 + 4d

Using elimination by subtracting one equation from another

5 = A1 + 4d

-(11.6 = A1 + d) You get -6.6 = 3d so d = -2.2

now that we have the difference substitute into the equation above 5 = A1 + 4 (-2.2)

solving for A1 5 = A1 - 8.8 A1 = 13.8

to check, we can use the other equation to check if our answers are correct:

11.6 = 13.8 - 2.2 - Yes, it is correct Final equation An = 13.8 + (n - 1) (-2.2)