determine the values of x and y so that the sequence -3/4 ;x ;y ;2/9 is a geometric sequence

Question

please explain how you would go about doing this sum.

Answer 1

In a geometric sequence, we can get from one term to the next by multiplying by a certain number, r, known as the common ratio.

 

So x = (-3/4)r, y = (-3/4)r² and 2/9 = (-3/4)r³

 

From the third equation,  r³ = -8/27.  So, r = -2/3

 

Therefore, x = (-3/4)r = (-3/4)(-2/3) = 1/2

 

    and      y = (-3/4)r² = (-3/4)(4/9) = -1/3

 

The first 4 terms of the sequence are -3/4, 1/2, -1/3, 2/9