Question

Which choice is the common difference between the terms of this arithmetic sequence?4x + 7y, 8x + 2y, 12x + -3y, 16x - 8y, 20x - 13y, ...

A.4x - 5y
B.-5x - 4y
C.4x + 5y
D.5x + 4y
E.5x - 4y

Answer 1

a1=4x+7y
a2=8x+2y
a3=12x-3y
a4=16x-8y
a5=20x-13y

a2-a1=(8x+2y)-(4x+7y)=8x+2y-4x-7y→a2-a1=4x-5y
a3-a2=(12x-3y)-(8x+2y)=12x-3y-8x-2y→a3-a2=4x-5y
a4-a3=(16x-8y)-(12x-3y)=16x-8y-12x+3y→a4-a3=4x-5y
a5-a4=(20x-13y)-(16x-8y)=20x-13y-16x+8y→a5-a4=4x-5y

The common difference between the terms of the arithmetic sequence is 4x-5y

Answer: Option A. 4x-5y